A symmetric density property for measurable sets
type: Item
instance of: scholarly article
title: A symmetric density property for measurable sets
zbMATH Open document ID: 0691.26005
published in: Real Analysis Exchange
publication date: 1989-01-01T00:00:00Z
review text: This is continuation of a previous authors' paper (summarized above). It is proved: Theorem 1. Let W and B be measurable subsets of a real interval whose union has full measure. If for each x, the set \(\{h>0:\quad x-h\in W\quad and\quad x+h\in B\}\) has density zero at zero, then these sets all have measure zero. Theorem 2. If a measurable real function has a nonnegative lower approximate symmetric derivative then it is non-decreasing on the set of points for which it is approximately continuous.
reviewed by: Pavel Kostyrko
Mathematics Subject Classification ID: 26A24
Mathematics Subject Classification ID: 26A48
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 28A20
zbMATH DE Number: 4130696
zbMATH Keywords: approximate continuity
zbMATH Keywords: density
zbMATH Keywords: measurable real function
zbMATH Keywords: approximate symmetric derivative
author: Chris Freiling
author: Dan Rinne
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4130696