Cantor四分集上的变换及其遍历测度
The transformations of Fourth-middle Cantor set and their ergodic measures

Keywords: Cantor四分集, 不变测度, 遍历测度,
Fourth-Middle Cantor set, invariant measure, ergodic measure

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Abstract:

该文给出了Tα(x)＝αx(mod 1)(α∈R＋)是Cantor四分集T(4，{0,2})上的变换的充要条件：Tα为T(4，{0,2})上的变换当且仅当α＝4n(n∈Z).并且研究了Tα的遍历测度的存在性.

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