The classical von Neumann–Oxtoby–Ulam Theorem states the following:
Given non-atomic Borel probability measures μ, λ on
In such that
there exists a homeomorphism
hof In onto itself fixing the boundary pointwise such that for any λ-measurable set S
It 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].