Continous measure-preserving maps onto Peano spaces

Alan Henry Schoenfeld

Vol. 58 (1975), No. 2, 627–642

DOI: 10.2140/pjm.1975.58.627

Abstract

In this paper we obtain measure-theoretic versions of some topological existence theorems relating to continuous maps, in particular the Hahn-Mazurkiewitz Theorem. Let X be a Peano Space and λ a Borel measure on X with λ(X) = 1. There is a continuous measure-preserving surjection from the unit interval (with Lebesque measure) to X if and only if the support of λ is X.

Mathematical Subject Classification

Primary: 54F25

Secondary: 28A65

Milestones

Received: 22 January 1974

Published: 1 June 1975