A strong Borel–Cantelli lemma for recurrence
Persson, Tomas LU
(2023)
In Studia Mathematica
268(1).
p.75-89
- Abstract
- Consider a dynamical systems ([0, 1], T, µ) which is exponentially mixing for L1 against bounded variation. Given a non-summable sequence (mk) of non-negative numbers, one may define rk(x) such that µ(B(x, rk(x)) = mk. It is proved that for almost all x, the number of k ≤ n such that Tk(x) ∊ Bk(x) is approximately equal to m1+· · ·+mn. This is a sort of strong Borel–Cantelli lemma for recurrence. A consequence is that (Formula Presented) for almost every x, where τ is the return time.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1f9ddbaf-d2b2-40bd-aef3-a551846fdcbb
- author
- Persson, Tomas
LU
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Studia Mathematica
- volume
- 268
- issue
- 1
- pages
- 75 - 89
- publisher
- Institute of Mathematics. Polish Academy of Sciences
- external identifiers
-
- scopus:85166136352
- ISSN
- 0039-3223
- DOI
- 10.4064/sm220216-2-7
- language
- English
- LU publication?
- yes
- id
- 1f9ddbaf-d2b2-40bd-aef3-a551846fdcbb
- alternative location
- https://arxiv.org/abs/2202.07344
- https://arxiv.org/abs/2202.07344
- date added to LUP
- 2023-10-03 20:56:15
- date last changed
- 2025-10-14 11:11:36
@article{1f9ddbaf-d2b2-40bd-aef3-a551846fdcbb,
abstract = {{Consider a dynamical systems ([0, 1], T, µ) which is exponentially mixing for L1 against bounded variation. Given a non-summable sequence (mk) of non-negative numbers, one may define rk(x) such that µ(B(x, rk(x)) = mk. It is proved that for almost all x, the number of k ≤ n such that Tk(x) ∊ Bk(x) is approximately equal to m1+· · ·+mn. This is a sort of strong Borel–Cantelli lemma for recurrence. A consequence is that (Formula Presented) for almost every x, where τ is the return time.}},
author = {{Persson, Tomas}},
issn = {{0039-3223}},
language = {{eng}},
number = {{1}},
pages = {{75--89}},
publisher = {{Institute of Mathematics. Polish Academy of Sciences}},
series = {{Studia Mathematica}},
title = {{A strong Borel–Cantelli lemma for recurrence}},
url = {{http://dx.doi.org/10.4064/sm220216-2-7}},
doi = {{10.4064/sm220216-2-7}},
volume = {{268}},
year = {{2023}},
}