An ergodic theorem for non-invariant measures

Details An ergodic theorem for non-invariant measures An ergodic theorem for non-invariant measures

2012-03-27

arxiv.org/abs/1203.6000v1

Mathematics

Dynamical Systems

16 pages

Scientific paper

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

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