Equipartitioning common domains of non-atomic measures
type: Item
instance of: scholarly article
title: Equipartitioning common domains of non-atomic measures
zbMATH Open document ID: 0548.60021
DOI: 10.1007/BF01164162
author: Theodore P. Hill
published in: Mathematische Zeitschrift
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173590
review text: If \(\mu_ 1,\mu_ 2,...,\mu_ n\) are non-atomic finite measures on the same measure space (X,\({\mathcal F})\), then there is a measurable partition \(A_ 1,...,A_ n\) of X such that \(\mu_ i(A_ i)\geq n^{- 1}h(\|\mu_ 1\|,...,\|\mu_ n\|)\) for all \(i=1,...,n\), where \(h(a_ 1,...,a_ n)\) is the harmonic mean \(n(a_ 1^{- 1}+...+a_ n^{-1})^{-1}\) of \(a_ 1,...,a_ n\) and \(\|\mu \|\) is the total variation of \(\mu\) ; moreover, this bound is best possible.
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 28C99
Mathematics Subject Classification ID: 28A99
Mathematics Subject Classification ID: 60A10
zbMATH DE Number: 3874310
zbMATH Keywords: measurable partition
zbMATH Keywords: total variation
MaRDI profile type: Publication
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OpenAlex ID: W2028581808
description: scientific article; zbMATH DE number 3874310