Acta mathematica scientia,Series A ›› 2002, Vol. 22 ›› Issue (4): 471-476.
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TU Jing-Hu, YANG Yuan-Qi
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Supported by:
国家自然科学基金资助（６０１７４０４８）
Abstract:
设犡是一完备可分度量空间，犓（ω）为Ｇｒａｆ随机模型下的随机递归集．该文构造了一列随机不变测度μ狀（狀≥１），它们是Ｈｕｔｃｈｉｎｓｏｎ确定模型下不变测度的推广；证明了存在一随机概率测度μ ，使得Ｓｕｐｐμ ＝犓（ω）且μ狀→μ （狀→∞）（弱收敛）；得到了μ狀的一些局部性质．
Key words: 统计自相似集；随机不变测度；弱收敛；局部性质
CLC Number:
TU Jing-Hu, YANG Yuan-Qi. Statistically Self-Similar Sets and Random Lnvariant Measures[J].Acta mathematica scientia,Series A, 2002, 22(4): 471-476.
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［１］ ＦａｌｃｏｎｅｒＫＪ．Ｔｈｅｇｅｏｍｅｔｒｙｏｆｆｒａｃｔａｌｓｅｔｓ．Ｏｘｆｏｒｄ：ＣａｍｂｒｉｄｇｅＵｎｉｖｅｒｓｉｔｙＰｒｅｓｓ，１９８５ ［２］ ＦａｌｃｏｎｅｒＫＪ．Ｒａｎｄｏｍｆｒａｃｔａｌｓ．ＭａｔｈＰｒｏｃＣｏｍｂＰｈｉｌＳｏｃ，１９８６，１００：５５９－５９２ ［３］ ＦａｌｃｏｎｅｒＫＪ．Ｔｅｃｈｎｉｑｕｅｉｎｆｒａｃｔａｌｇｅｏｍｅｔｒｙ，Ｊｏｈｎ Ｗｉｌｅｙ ＆ｓｏｎｓＬｔｄ．ＢａｆｆｉｎｓＬａｎｓ．Ｃｈｉｃｈｅｓｔｅｒ，１９９７ ［４］ ＧｒａｆＧ．Ｓｔａｔｉｓｔｉｃａｌｌｙｓｅｌｆｓｉｍｉｌａｒｆｒａｃｔａｌｓ．ＰｒｏｂａｂＴｈＲｅｌＦｉｅｌｄｓ，１９８７，７４：３５７－３９２ ［５］ ＨｕｔｃｈｉｎｓｏｎＪＥ．Ｆｒａｃｔａｌｓａｎｄｓｅｌｆｓｉｌａｒｉｔｙ．ＩｎｄｉａｎａＵｎｉｖＭａｔｈＪ，１９８１，３０：７１３－７４７
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