| 相伴于随机自相似分形的随机测度的强测度的收敛性 |
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| 引用本文： | 梁洪亮. 相伴于随机自相似分形的随机测度的强测度的收敛性[J]. 湘潭大学自然科学学报, 2005, 27(3): 20-23 |
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| 作者姓名： | 梁洪亮 |
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| 作者单位： | 商丘师范学院,数学系,河南,商丘,476000 |
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| 基金项目： | 河南省高校青年骨干教师资助项目(豫高教2003(100)) |
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| 摘 要： | 构造了随机自相似分形及其上的记忆函数,并得出了有关结论,在此基础上,定义一个随机概率测度dΦn(τ)= Kn(τ)dτ,Φn(τ)弱收敛于Φ,进一步可得到强测度序列Ψn(·)=EΦn(·),则|Ψn|弱收敛于Ψ=EΦ.
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| 关 键 词： | 随机自相似分形 记忆函数 测度 收敛 |
| 文章编号： | 1000-5900（2005）03-0020-04 |
| 收稿时间： | 2004-08-25 |
| 修稿时间： | 2004-08-25 |
Convergence of the Intensity Measure of Random Measure Associated to the Random Self-Similar Fractal |
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| LIANG Hong-liang. Convergence of the Intensity Measure of Random Measure Associated to the Random Self-Similar Fractal[J]. Natural Science Journal of Xiangtan University, 2005, 27(3): 20-23 |
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| Authors: | LIANG Hong-liang |
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| Abstract: | The construction of the random self-similar fractals E(n) and memory functions on E(n) are given. Based on it, we define a random probability measure Φn(τ)on E(n),{Φn(τ)} converges weakly a.s. to Φ. Furthermore, let Ψn(·)=EΦn(·), then Ψn is the intensity measure of the random measure Φn. Moreover, the sequence {Ψn} is weakly convergent and Ψ=limΨn=EΦ. |
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| Keywords: | random self - similar fractals memory functions measures convergence |
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