English

A double return times theorem

Dynamical Systems 2021-05-04 v2

Abstract

We prove that for any bounded functions f1,f2f_1, f_2 on a measure-preserving dynamical system (X,T)(X,T) and any distinct integers a1,a2a_1, a_2, for almost every xx the sequence f1(Ta1nx)f2(Ta2nx) f_1(T^{a_1 n}x) f_2(T^{a_2 n}x) is a good weight for the pointwise ergodic theorem.

Keywords

Cite

@article{arxiv.1506.05748,
  title  = {A double return times theorem},
  author = {Pavel Zorin-Kranich},
  journal= {arXiv preprint arXiv:1506.05748},
  year   = {2021}
}

Comments

v2: 8 pages, improved typography

R2 v1 2026-06-22T09:56:07.351Z