| 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,焦美芝.相伴于随机自相似分形的随机测度的强测度的收敛性[J].纯粹数学与应用数学,2005,21(3):263-267. |
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| 作者姓名： | 梁洪亮 焦美芝 |
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| 作者单位： | 商丘师范学院数学系,商丘,476000;商丘师范学院财务处,商丘,476000 |
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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,我们可以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： | 1008-5513（2005）03-0263-05 |
| 收稿时间： | 2004-12-30 |
Convergence of the intensity measure of random measure associated to the random self similar fractal |
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| LIANG Hong-liang,JIAO Mei-zhi.Convergence of the intensity measure of random measure associated to the random self similar fractal[J].Pure and Applied Mathematics,2005,21(3):263-267. |
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| Authors: | LIANG Hong-liang JIAO Mei-zhi |
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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 defined a random probability measure Φn(τ) on E(n), {Φn(τ)} converges weakly a.s.to Φ. Furthermore, let Φn(·)=EΦn(·), the 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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