关于IFS的一个经典遍历定理的注记

给出了Elton定理不成立的点构成的集合的性质:通过构造符号空间中的柱集，证明了对一个具有概率的压缩IFS，连续函数g满足$ \int_X g \mathrm{~d} \nu_1 \neq \int_X g \mathrm{~d} \nu_2$，ν₁和ν₂表示IFS中2个不同的不变测度，则Elton定理不成立的点构成的零测集要么是空集，要么是具有满Hausdorff维数和满拓扑熵的集合。

A Note on a Classical Ergodic Theorem for IFS

The properties of the set of points where Elton's theorem does not hold are given. By constructing cylinder sets in symbolic space, it is proved that for a contractive IFS with probabilities and a continuous function g sa-tisfying that $ \int_X g \mathrm{~d} \nu_1 \neq \int_X g \mathrm{~d} \nu_2$, where ν₁ and ν₂ are any two different invariant measures of the IFS, the zero measure invariant set composed of points where Elton's theorem does not hold is either empty or carries full Hausdorff dimension and topological entropy.