2021 EXCEPTIONAL POINTS FOR DENSITIES GENERATED BY SEQUENCES
Tomasz Filipczak, Grażyna Horbaczewska
Author Affiliations +
Real Anal. Exchange 46(2): 305-317 (2021). DOI: 10.14321/realanalexch.46.2.0305

Abstract

In spite of the Lebesgue density theorem, there is a positive δ such that, for every measurable set A with λ(A)>0 and λ(\A)>0, there is a point at which both the lower densities of A and of the complement of A are at least δ. The problem of determining the supremum δH of possible values of this δ was studied by V. I. Kolyada, A. Szenes and others, and it was solved by O. Kurka. Lower density of A at x is defined as a lower limit of λ(A[x-h,x+h])/2h. Replacing λ(A[x-h,x+h])/2h by λ(A[x-tn,x+tn])/2tn for a fixed decreasing sequence t tending to zero, we obtain a definition of the constant δt. In our paper we look for an upper bound of all such constants.

Citation

Download Citation

Tomasz Filipczak. Grażyna Horbaczewska. "EXCEPTIONAL POINTS FOR DENSITIES GENERATED BY SEQUENCES." Real Anal. Exchange 46 (2) 305 - 317, 2021. https://doi.org/10.14321/realanalexch.46.2.0305

Information

Published: 2021
First available in Project Euclid: 8 November 2021

MathSciNet: MR4336559
zbMATH: 1484.28002
Digital Object Identifier: 10.14321/realanalexch.46.2.0305

Subjects:
Primary: 28A99

Keywords: density points , differentiation basis , exceptional points

Rights: Copyright © 2021 Michigan State University Press

JOURNAL ARTICLE
13 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.46 • No. 2 • 2021
Back to Top