Real partitions of measure spaces
type: Item
instance of: scholarly article
title: Real partitions of measure spaces
zbMATH Open document ID: 0832.28012
DOI: 10.1007/BF02104943
published in: Siberian Mathematical Journal
publication date: 1995-09-20T00:00:00Z
review text: In this short note the author defines the notion of real partition and with its help existence is proved for measure-preserving mappings of several probability spaces onto the unit interval with the Lebesgue measure. A real partition of a probability space \((X, {\mathcal A}, \mu)\) is defined to be a partition \((D_t)_{t \in [0,1]}\) of the space, such that \(\mu (A^-_t) = \mu (A^+_t) = t\) for all \(t \in [0,1]\), where \(A^-_t = \cup_{s < t} D_s\) and \(A^+_t = \cup_{s \leq t} D_s\). The main theorem shows that: For every complete nonatomic probability space which includes a Cantor set, there exists a measure-preserving epimorphism of the space onto the unit interval with the Lebesgue measure.
Mathematics Subject Classification ID: 28A99
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 794628
zbMATH Keywords: real partition
zbMATH Keywords: measure-preserving mappings
zbMATH Keywords: probability spaces
author: Vladimir G. Troitsky
reviewed by: Octavian Lipovan
MaRDI profile type: Publication
cites work: Q3825006
cites work: Q5719719
cites work: Q4711784
cites work: Reduction of nonholonomic variation problems to isoperimetric ones and connections in principal bundles
cites work: On a constrained variational problem and the space of horizontal paths
full work available at URL: https://doi.org/10.1007/bf02104943
OpenAlex ID: W2046838141
description: scientific article; zbMATH DE number 794628