A note an homeomorphic measures on topological groups

Abstract

The classical von Neumann–Oxtoby–Ulam Theorem states the following:Given non-atomic Borel probability measures μ, λ on In such thatthere exists a homeomorphism h of In onto itself fixing the boundary pointwise such that for any λ-measurable set SIt is known that the above theorem remains valid if In is replaced by any compact finite dimensional manifold [2], [4] or with I∞, the Hilbert cube, [8].