Vol. 58, No. 2, 1975

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ISSN: 0030-8730
Continous measure-preserving maps onto Peano spaces

Alan Henry Schoenfeld

Vol. 58 (1975), No. 2, 627–642
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
Authors
Alan Henry Schoenfeld