В следующем пункте мы применим этот критерий к установлению важных парных классов функций
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
, для которых интеграл Стилтьеса существует.
I. Если функция
![](data:image/png;base64,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)
непрерывна, а функция
![](data:image/png;base64,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)
имеет ограниченное изменение, то интеграл Стилтьеса
![](data:image/png;base64,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)
(5)
существует.
Сначала предположим, что
![](data:image/png;base64,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)
монотонно возрастает: тогда примени критерий предыдущего пункта. По произвольно заданному
![](data:image/png;base64,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)
ввиду равномерной непрерывности функции
![](data:image/png;base64,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)
найдется такое
![](data:image/png;base64,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)
, что в любом промежутке с длиной, меньшей
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAATCAYAAABPwleqAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADiSURBVDjLY2hsbGQgFzMMTs1AwIiMidZcneViJMvA8Bqo6R8U/zeObvAhqLk+z8NQVtZjZVpHBw+cDzLIOHoBYc31sZLGDMa7YsvLpbA5l6Czy8tjpYwZGO7KuuWU4DIAZyBFGTMsZJA1Pmksy3CSQcZjT1p5OS9ezXBNwACCBQ7EC2AXFOPVnOMmW4IeKB0daTweMgx7GIyjFuLUDAlR2ZseefWG2PyOHk0omoG2FjMwGN8FhTCyN8Dish67YdGGVXNDtLEPyK+w0CWkEcPP0cYMC5BS1D9Zj7yiIZiraKoZAEh9jF9/YZHvAAAAAElFTkSuQmCC)
, колебание
![](data:image/png;base64,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)
будет меньше
![](data:image/png;base64,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)
. Пусть теперь промежуток
![](data:image/png;base64,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)
произвольно разбит на части так, что
![](data:image/png;base64,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)
. Тогда все
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
,
откуда и следует выполнение условия (4), а стало быть и существование интеграла.
В общем случае, если функция
![](data:image/png;base64,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)
имеет ограниченное изменение, она представима в виде разности двух ограниченных возрастающих функций:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIMAAAAXCAYAAAAoavwzAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAANoSURBVGje7Zo/btswFMZZz8kBYpS5Q8QcIXA0JGOHWPDUwkMQaEgGDQGiePPQXKBZki5Fr1D3BLlBgeYEzhXU1pQsiaIeKfJJrgRBw4MRmyK/3+PHvwpZLBZkiCF41K+AkHdNlmstEQb6+sCgK1er8SCYjRnz7kzKeozdzYJg3MUkmnL0gUHHUa9xwn7MwvDApHwYzg7i8h1Lpg1HHxh0HGgBG3eFpo0XRDAv7FIibTn6wKDiQDV+e3niUDZ9wDw7ZfTh5PLW6UISsRx9YIA4CK4S8sy8+zPMs/ceOyNs+tyFRGI5+sAAcVhXwKcXh9AX1w+PMAJC3z2ixHmxndaajjocfWCAOLTHDyh0iUjL6L6rC1B1ZILCpkPbYrDRbmJKDAfcyAU73zz0R4i//JO6/nU8tRD2KgtIvudl6ZqvQ7zR7DvqrubL5V6+kyWv8tSmSoZxYjSalVOkxFGXAT3CLbXrGASOCOCIdBwKYXSduiWphL4V/y4LSONqQm/4OpR8ek/wsaacSI+RJykhxQDqMtVsk0gsA9bMGO0mDBiOwo/L5XzPfU9+0snVTVFs3mCVgGTqIm9iHSZmwIaJZttEYhi2Zo5szIzVbmoGW46yOEpW3E3cyUEw3+diRZAqAekzqs5uepkw0Qw9r+PAMqCMnGsfQdrl3NiYIeO4CM+tzSC6SeXo5Hf6SzWN+RP26fiYfkuPLDKAavNVa5nQaM4SLiVNx4FlwO/oyVqZ76TDfsd7CGmEN90X8NXm4enjPAj2odEIJSJ1LXcq3/TEIqn7ndfBBYlld3Esq9LMDXF6yL4UzCAnoiWGKu2+637g7SR6nZWOoS5H6TgSbza2LuVOhKYnPorFKdJ36bXo6nw0lnfEyUWHepRjjmRVmiEzyBxtMAjaI0H7SLUk8htDaEYF+iICOKIqjtJtlvhAnqDibVvsqBpXoE2ez000q8yA5WiKwTTfWce77sf0WLiLvihvRoJgLG5YVKPAY/SzbUJsXrMaX6caaFaZAcPRFIOkfVSVb/69asPKGWzflUAcpHITp5gO07deNv9QgXm7VhUmmvmuemOGR+jVsw1H0wzgcRQ4ScTHTWf6lZtml31R392Ga6e8tv3PyAwj3L5hONpgyPYAW7Oo2m+iL1p/6zZEd2JIwhCDGYYoxz9onYQGT2CDVwAAAABJRU5ErkJggg==)
. В соответствии с этим преобразуется и сумма Стилтьеса, отвечающая функции
![](data:image/png;base64,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)
:
![](data:image/png;base64,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)
.
Так как по уже доказанному каждая из сумм
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAAXCAYAAADpwXTaAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADqSURBVDjLY2hsbGSgFmYYNWwkGAYEjLgw0YaBFFdnuRjJMjC8BrL/YWLZ1x559YZEGZbjJlvCwGB8J7a+XhLE7+hI43EzdqtNKy/nJcmb9ZHGvsgGIVlQLOuWU0y0YSAXeMgw7MGmCWQYg3HUQqINq8/zMJRlkL2JHh7YLMEVEWiGMbwxjqz3xfQ6ItDBhssy7AYGx1304EB1AUiRjMceUGCDbIYYxPDPOLrBB9217nLGs3AaBnZFfaykMQPDHUQywIwMog0jFg9ew8rL03iBhs2OLS+XotiwaGOGBeAwlfXYndbRwTPCyjMAoBlx3nEdIe8AAAAASUVORK5CYII=)
и
![](data:image/png;base64,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)
при
![](data:image/png;base64,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)
стремится к конечному пределу, то это справедливо и относительно суммы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAPCAYAAADtc08vAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC0SURBVDjLY2hsbGSgBDPQzAAgYMSF8RoAUlCd5WIky8DwGsj+h4llX3vk1RviNCDHTbaEgcH4Tmx9vSSI39GRxuNm7FabVl7OS9AL9ZHGvsiakQwtlnXLKcZrAMgmDxmGPdgUggxgMI5aiNeA+jwPQ1kG2ZvI/iNkMBYDGN4YR9b7YnoLNeBwe0GWYTeDjMceUICBYgOimeGfcXSDD1HpoL4+VtKYgeEOIsowA5R+KXHoGAAA1ihPPPABlCkAAAAASUVORK5CYII=)
, что и требовалось доказать.
Можно ослабить условия, налагаемые на функцию
![](data:image/png;base64,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)
, если одновременно усилить требования к функции
![](data:image/png;base64,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)
:
Если функция
![](data:image/png;base64,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)
интегрируема в
![](data:image/png;base64,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)
в смысле Римана, а
![](data:image/png;base64,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)
удовлетворяет условию Липшица:
![](data:image/png;base64,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)
(6)
то интеграл (5) существует.
Для того чтобы опять иметь возможность применить установленный выше критерий, предположим сначала функцию
![](data:image/png;base64,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)
не только удовлетворяющей условию (6), но и монотонно возрастающей.
Ввиду (6), очевидно,
![](data:image/png;base64,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)
, так что
![](data:image/png;base64,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)
.
Но последняя сумма при
![](data:image/png;base64,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)
и сама стремится к 0 вследствие интегрируемости (в смысле Римана) функции
![](data:image/png;base64,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)
, а тогда стремится к нулю и первая сумма, что доказывает существование интеграла (5).
В общем случае функции
![](data:image/png;base64,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)
, удовлетворяющей условию Липшица (6), представим в виде разности
![](data:image/png;base64,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)
Функция
![](data:image/png;base64,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)
, очевидно, удовлетворяет условию Липшица и в то же время монотонно возрастает. То же справедливо и для функции
![](data:image/png;base64,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)
, так как, в силу (6), при
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
В таком случае рассуждение завершается, как и выше.
III. Если функция
![](data:image/png;base64,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)
интегрируема в смысле Римана, а функция
![](data:image/png;base64,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)
представима в виде интеграла с переменным верхним пределом:
![](data:image/png;base64,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)
(7)
где
![](data:image/png;base64,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)
абсолютно интегрируема, в промежутке
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACMAAAAXCAYAAACBMvbiAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAGCSURBVEjH7ZYxboMwFIZf9+QAqeJDwNs7VchDLgAWYxmqiKGpxFBVDhtL7pCcIzlBb1CJnCA9Q1OMQSZWIQ4iztAivQXb7332+9+zIU1TqK347prWHBvS2uKcTAoQNsXgd2nI1teCiSl5qeIcAYNNKwzx5otrQehWbv7PwZhozwpMlkUjSmArdNHlz2qaAiQrGnPn5jCchxMX3G3I+WRQGL0vmPSgJcOZCNS15mIY4WTukYXsC+TgefgOU7qLsmx0rlKQsScEyMu1v6y5CCZJojGdwq5ugOLoC+f7c6ms5wFgLtLEY+oQgC9ky1lvGDlZdeKySgo43WlbinS43jClQ8B9U4Bvz48uAfejS5QqRSqwXEc+9coyhtEnqpSpfyZVJDSnn3BvGOEsScL7SohHIUrfVzvUK0WvIil+qZ3eMDJN1Q1eOPO570gg5bgS5kEPxhDWJrf/4E1P7J779KGr01qBqaok7/v2MYF5tfXS64QxzfWAL72TOFYeUcYn9g/TYj+l6Vs35eHdZgAAAABJRU5ErkJggg==)
, то интеграл (5) существует.
Пусть
![](data:image/png;base64,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)
, так что
![](data:image/png;base64,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)
монотонно возрастает. Если
![](data:image/png;base64,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)
интегрируема в собственном смысле и, следовательно, ограничена:
![](data:image/png;base64,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)
то для
![](data:image/png;base64,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)
Имеем
![](data:image/png;base64,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)
Таким образом, в этом случае
![](data:image/png;base64,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)
удовлетворяет условию Липшица, и интеграл существует в силу 2.
Предположим теперь, что
![](data:image/png;base64,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)
интегрируема в несобственном смысле. Ограничимся случаем одной особой точки, скажем
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAATCAYAAABLN4eXAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADJSURBVDjLY2hsbGQgFTMMnCYgYARiJhBNlKaOjjQeD1mG3UAN/2TdcopJcl6UsWyvR169IdGa6utjJY0YjHbH1tdLEq8p0tiXwThqIdRfWP2GxWkMC42jo1ONGRjugPzGIOOxJ62jgwenJpDTgIrvMjAY3wY5rz7Pw1CWgeGNcXSDD25NYKdFL0A3BK8miNMQCqqzXIxkGWRvoockzlADBQDIEGSbMTQ1xBp7I4dajptsMcxveEMv2phhAVDDXzDGYsMgSOU00wQA46RbJHPiG00AAAAASUVORK5CYII=)
. Прежде всего, по произвольно взятому
![](data:image/png;base64,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)
выберем
![](data:image/png;base64,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)
так, чтобы было
![](data:image/png;base64,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)
(8)
где
![](data:image/png;base64,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)
- общее колебание функции
![](data:image/png;base64,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)
в рассматриваемом промежутке.
Разобьем промежуток
![](data:image/png;base64,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)
по произволу на части и составим сумму
![](data:image/png;base64,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)
Она разлагается на две суммы
![](data:image/png;base64,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)
, из коих первая отвечает промежуткам, целиком содержащимся в промежутке
![](data:image/png;base64,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)
, а вторая - остальным промежуткам. Последние наверное содержаться в промежутке
![](data:image/png;base64,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)
, если только
![](data:image/png;base64,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)
; тогда, в силу (8),
![](data:image/png;base64,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)
С другой стороны, так как в промежутке
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEQAAAAtCAYAAAAX6M0gAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAANUSURBVGje7Zq9btpQFMcPrCWdypCWy9SpG75d26ZSZFzlY4sUY3msB4QYkkgeosTOxtA+QLsQMkW8QQmdW+UJWkFfIMorNO29NtcYy752CsYp10hnAIzM+XE+/udc4OzsDHKbWg6BB4Q8iiFWWAVH+6G+9YuRQCxLX8cAY3Lhb79h3d5aBSANDN2gb4AbPT4QrFmipEaUvzmQHEgORDwg/UDX8HcU4YBQWaBhOC8A3NGuQSHQ524nQbebzWNJKCC2hrexZm83JLgAjAdEOoyoVJjIiF9IaR8IBaTZbD5nzpPvf6pb1rrjT1upIUA/lbZVE66GWCreAcBjBsN7DSlXRqdTEg6Imy7aeUCZ9qLSZaWBeOlC6gh7zTT1pxKg66h0yRxIP8VBMSxdWjI64qVLpkA6HaNURzAgMO54ITzX0IYbXf/9lAoM4+6VCIgkNez0pk30kRfCi7Lj5qbE6y5x/vou2HhRLr/9klaeSyBd+cM6LSPpcggVZchLF+bvk0f4e/C6e6cMrQP+5VHYkiU0z0kX4C1m0kohbspU65/nAkKLo/MLuLL4RpbxaVzxYm0Ra9p7qiKdz1bqQ8M01zLvTvMAMU1jrV4pDBl9TxrLrcP4tlgYk04woinjKki49bfJ4EAGCdd9mQGhqbEfED+smgcdi0oXnm7wQj244ptd93UD36mY1BYOJKzXu9Vcuo4rlFQx+p2nn6tC9ce8HYcLL2ALB0Kd8i9kDWPvsVyBr0G5HNddwiLtQdeQKB3i7Bek/Qsafqa592xSHP/QQqmq7i8dFp62jreKWO2x99yC7NaS/wAI1SEbg9CdA3FsGoJ4pFpqzYUyUyhvwpydqQ0J2uHygMTqkGggCXO6aKnKm2Wo0aj73+dwLVUgk84xyioC6HTraRwyM9XUk904KKlHSFbmtP/qy08sVdsKOqD7VaxaO0ICsXXllT9NmT4KO6YUAki0TIiTBIIA8RR0zCF9QiDpjP/LNEdBo3eXScb/cgl/m3v8f8jmHlqhD0la/8qf7VIYVAn7U4XXelcaCHX8RK3tIrl1xMQZSR2sqNZr4YAwGHS2mrXZ6VwYIFSIJdmfCFdD/mncSHIMIcq/EJ01RmyETAckUf6F2I0EklsOJAeSxP4Cy+w4HXJLXHIAAAAASUVORK5CYII=)
функция
![](data:image/png;base64,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)
интегрируема в собственном смысле, то по доказанному при достаточно малом
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAATCAYAAABPwleqAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADzSURBVDjLY2hsbGQgFzMMTs1AwATCJGsuL4+VMmZguM3AIPvKI6/ekGjNHR1pPB5yJjNj6+sl6/M8DI3d8lJI0pyX1yABYldnuRh5RNbbkezn/wwMjBFGsn0kORsaWIw5brIlDAzGd0HOJ0kz0LnGcgxyN2RlTbaRpLm8PFQaGNJ3jGMbvKM9PJLTOjp4iNJcnhbK5y7DuEfWI68IHOoe0clExTMDOIAYFjHIeu4C2VZfHyvp5pYXBpPDqRkkWRtp6AcMoNswP0LiOCcVKMec52ac4lHcYIBVc5aHbBE4NSEpANkMSWUMf2Q9soqGSK6iqWYA3emY4ki18OkAAAAASUVORK5CYII=)
и сумма
![](data:image/png;base64,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)
станет меньше
![](data:image/png;base64,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)
. Отсюда следует (4), что и требовалось доказать.
В общем случае, когда функция
![](data:image/png;base64,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)
абсолютно интегрируема в промежутке
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACMAAAAXCAYAAACBMvbiAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAGtSURBVEjH7ZZNTsJAFMcfrtE9keEO9B3ADWkmUZcs2oalXRjSBZh0YeLArhvvAFwDvIAnMAEvQLwC6rwpk8LEltIUMFGSlwCdee837+PfgeFwCNrkpyLtbG2VzWdlWlqcrUUuwlg+/JS2AvRGh4IJOOupGBQL3XEqDLO7/UNBmKYO/+dgNvqiclKYKPKrnMGUeoLxoPcryuQie+aBaJ4cRohOzQJr2hGiViqMqQt5NEg4eEvykKVbe8OQo67N+rEusKVt4xMwPvWjqLprUtDz7hBgrvbW+czcsxdMGPrnvA4zLYCUeun8fVcp9ToAnFOZRMCbDOADvcFNIRhKa7w4UWI1JRLOdJpWIhOuMIxyCLjYbMDH+5bFwHrNasqkRElg2teAxps5WblhzIW+376QWXnZ9c4yp+inDO8N4yGMwHIn1MBh2L6UaV7I71/UlI6TnFBPi/496OA1BdD/x80f905hGOU0frOuyJkjnGY8GYnjdWMuzXKqg+i9GZksXfTo9MLhV1lKexSY9ZTMi9598sA8HOum51owSYXJW+sSb3pbcY5yicqdsX+YFPsGwE1ZeniChIkAAAAASUVORK5CYII=)
, мы рассмотрим функции