An ergodic theorem for non-invariant measures

Maria Carvalho; Fernando Moreira

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arXiv · 1203.6000

An ergodic theorem for non-invariant measures

Maria Carvalho·Fernando Moreira

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Abstract

Given a space $X$, a $σ$-algebra $\mathfrak{B}$ on $X$ and a measurable map $T:X \to X$, we say that a measure $μ$ is half-invariant if, for any $B \in \mathfrak{B}$, we have $μ(T^{-1}(B)\leq μ(B)$. In this note we present a generalization of Birkhoff's Ergodic theorem to $σ$-finite half-invariant measures.

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Maria Carvalho, Fernando Moreira. 2012-03-27. An ergodic theorem for non-invariant measures. https://arxiv.org/abs/1203.6000

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