1. Strongly mixing sequences of measure preserving transformations
- Creator:
- Behrens, Ehrhard and Schmeling, Jörg
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- ergodic transformation, strongly mixing, Birkhoff ergodic theorem, and Komlós theorem
- Language:
- English
- Description:
- We call a sequence $(T_n)$ of measure preserving transformations strongly mixing if $P(T_n^{-1}A\cap B)$ tends to $P(A)P(B)$ for arbitrary measurable $A$, $B$. We investigate whether one can pass to a suitable subsequence $(T_{n_k})$ such that $\frac{1}{K} \sum _{k=1}^K f(T_{n_k}) \longrightarrow \int f \mathrm{d}P$ almost surely for all (or “many”) integrable $f$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public