统计自相似集和测度的概率特征

The Probability Character of Statistically Self-Similar Sets And Measures

证明了统计自相似集和测度是由一族独立同分布的随机压缩算子｛fσ，σ∈D｝所构成的随机递归集和它的分布．此处fσ是概率空间（Ω，F，P）到con（E）的随机元，con（E）是完备可分距离空间E到E的压缩算子全体．

In this paper,we have proved that the statistically self-similar set is generated by a collection of random contraction operators {fσ,σ∈D},where fσ is a random elements from probability space (Ω,P) to con (E),and con (E) denotes all contraction opera-tors from complete separable metric space E to E.