| 论绝对连续函数 |
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| 引用本文： | 宋亦洪. 论绝对连续函数[J]. 贵州师范大学学报(自然科学版), 1997, 15(2): 68-72 |
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| 作者姓名： | 宋亦洪 |
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| 作者单位： | 贵州师大数学与计算机科学系 |
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| 摘 要： | 本文在测度论的意义下讨论了传统的绝对连续函数这一概念，定义了一种称为依测度绝对连续的概念，并讨论了相应的若干性质，证明了在一维的情形下，依测度绝对连续与通常的绝对连续这两个概念是等价的。给出了当绝对连续函数列收敛时，其收敛的函数是绝对连续函数的条件
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| 关 键 词： | 绝对连续函数，Lebesque测度，可测集 |
ON THE ABSOLUTE CONTINUOUS FUNCTION |
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| Song Yihong. ON THE ABSOLUTE CONTINUOUS FUNCTION[J]. Journal of Guizhou Normal University(Natural Sciences), 1997, 15(2): 68-72 |
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| Authors: | Song Yihong |
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| Abstract: | The purpose of this paper is to study the clussic absolute continuous function, in the sense of measure theory The author defines a absolute continuous function in measure, discusses some characters of it, and shows that the concept of absolute continuous function is equivalent to that of absolute continuous function in measure on one-dimensional Euclidean space In addition, the author gives a condition on which the limit function of pointwise convegent absolute continuous function is also a absolute continnous function |
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| Keywords: | Absolute continuous function Lebesque measure measurable set |
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