| 关于自保形测度与Lebesgue测度的等价性 |
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| 引用本文： | 张玉芹.关于自保形测度与Lebesgue测度的等价性[J].数学杂志,2001,21(2):151-154. |
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| 作者姓名： | 张玉芹 |
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| 作者单位： | 武汉大学数学系 |
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| 基金项目： | Supported by the Special Funds for Major State Basic Research Projects of China. |
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| 摘 要： | 本文我们研究了自保形测度与Lebesgu测度的关系，对Yuvla Peres等的结果进行了推广，证明了自相似测度要么是奇异的，要么关于Lebesgue测度 绝对连续的，并且若将Lebesgue测度限制在自相似测度的紧支撑上，则其关于非奇异的自相似测度是绝对连续的。
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| 关 键 词： | 自保形测度 Lebesgue测度 开集条件 紧支撑 等价性 绝对连续 |
| 文章编号： | 0255-7797(2001)02-0151-04 |
ON THE EQUIVALENCE OF SELFCONFORMAL MEASURE TO LEBESGUE MEASURE |
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| ZHANG Yu-qin.ON THE EQUIVALENCE OF SELFCONFORMAL MEASURE TO LEBESGUE MEASURE[J].Journal of Mathematics,2001,21(2):151-154. |
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| Authors: | ZHANG Yu-qin |
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| Abstract: | In this article,we show that:the self-similar measure is either singular or absolutely continuous with respect to Lebesgue measure and the converse is true when Lebesgue measure is restricted to the compact support of the self-similar measure, which generalizes the result of Yuval Peres, etc., see1]. |
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| Keywords: | self-conformal measure Lebesgue measure open set condition |
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