Published paper

Measure theoretic laws for lim sup sets

Victor Beresnevich, Detta Dickinson, Sanju Velani

MSC 2020

11J8311J1311K6028A7828A80

Published version ↗Open DOI ↗arXiv record ↗

Publication metadata

Journal citation: Memoirs of the American Mathematical Society 179(846), x+91 (2006)
Publication date: 2006
DOI: 10.1090/memo/0846 ↗
arXiv counterpart: arXiv:math/0401118v3 ↗
MSC 2020: 11J83, 11J13, 11K60, 28A78, 28A80
As specified in the publication (MSC 2000): 11J83, 11J13, 11K60, 28A78, 28A80 ↗Full author manuscript, page 4The publication does not label primary versus secondary roles; all five codes carry forward unchanged.
Official MSC conversion: MSC 2000 → MSC 2010 ↗MSC 2010 → MSC 2020 ↗

Abstract

The memoir establishes general measure laws for limsup sets. Proposition 1 gives the local positive-density-to-full-measure principle reproduced as Kleinbock–Wang Lemma 3.2.

Role in dependence graphs

Proof-critical source

Bounded trajectories of quasi-rays

This paper is included only for the following marked statement:

Proposition 1 · printed p. 29; arXiv PDF p. 35A uniform positive-density lower bound in every sufficiently small ball forces a Borel set to have full measure for a finite doubling measure. Kleinbock–Wang reproduce it as Lemma 3.2.

Proof-critical source

Khintchine-type theorems for weighted uniform inhomogeneous approximations via transference principle

This paper is included only for the following marked statement:

Proposition 1 · printed p. 29 / author-manuscript PDF p. 35Positive local density implies full measure.

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