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On maximizing measures of homeomorphisms on compact manifolds

Fábio Armando Tal, Salvador Addas-Zanata (2008)

Fundamenta Mathematicae

We prove that given a compact n-dimensional connected Riemannian manifold X and a continuous function g: X → ℝ, there exists a dense subset of the space of homeomorphisms of X such that for all T in this subset, the integral X g d μ , considered as a function on the space of all T-invariant Borel probability measures μ, attains its maximum on a measure supported on a periodic orbit.

On measure theoretical analogues of the Takesaki structure theorem for type III factors

Alexandre Danilenko, Toshihiro Hamachi (2000)

Colloquium Mathematicae

The orbit equivalence of type I I I 0 ergodic equivalence relations is considered. We show that it is equivalent to the outer conjugacy problem for the natural trace-scaling action of a countable dense ℝ-subgroup by automorphisms of the Radon-Nikodym skew product extensions of these relations. A similar result holds for the weak equivalence of arbitrary type I I I 0 cocycles with values in Abelian groups.

On measure-preserving transformations and doubly stationary symmetric stable processes

A. Gross, A. Weron (1995)

Studia Mathematica

In a 1987 paper, Cambanis, Hardin and Weron defined doubly stationary stable processes as those stable processes which have a spectral representation which is itself stationary, and they gave an example of a stationary symmetric stable process which they claimed was not doubly stationary. Here we show that their process actually had a moving average representation, and hence was doubly stationary. We also characterize doubly stationary processes in terms of measure-preserving regular set isomorphisms...

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