For ergodic Zd and Rd-actions, we obtain a pointwise lower bound for the supremum of ergodic averages. For Zd-actions in the case when the supremum is taken over multi-indices exceeding n→ located in a certain sector, the resulting inequality is not improvable over n→ in the class of all averaging integrable functions.
- Individual ergodic theorem
- Rates of convergence in ergodic theorems
- Wiener-wintner ergodic theorem
- individual ergodic theorem
- Wiener-Wintner ergodic theorem
- rates of convergence in ergodic theorems
- 1.01 MATHEMATICS