Vol. 77, No. 2, 1978

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ISSN: 0030-8730
Homeomorphic measures in the Hilbert cube

John C. Oxtoby and Vidhu S. Prasad

Vol. 77 (1978), No. 2, 483–497
Abstract

A Borel probability measure μ in the Hilbert cube is homeomorphic to the usual product measure if and only if it is positive for nonempty open sets and zero for points. The transformation can be effected by a homeomorphism equal to the identity on any prescribed μ-null Z-set. Several extension, approximation, and embedding theorems are obtained as applications.

Mathematical Subject Classification 2000
Primary: 28A35
Secondary: 28C15
Milestones
Received: 3 October 1977
Published: 1 August 1978
Authors
John C. Oxtoby
Vidhu S. Prasad