Double ergodicity of nonsingular transformations and infinite measure-preserving staircase transformations

Double Ergodicity of Nonsingular Transformations and In nite measure-preserving Staircase Transformations

A nonsingular transformation is said to be doubly ergodic if for all sets A and B of positive measure there exists an integer n > 0 such that (T n(A) \ A) > 0 and (T n(A) \ B) > 0. While double ergodicity is equivalent to weak mixing for nite measure-preserving transformations, we show that this is not the case for in nite measure preserving transformations. We show that all measure-preserving ...

Some Observations on Dirac Measure-Preserving Transformations and their Results

Dirac measure is an important measure in many related branches to mathematics. The current paper characterizes measure-preserving transformations between two Dirac measure spaces or a Dirac measure space and a probability measure space. Also, it studies isomorphic Dirac measure spaces, equivalence Dirac measure algebras, and conjugate of Dirac measure spaces. The equivalence classes of a Dirac ...

Infinite Measure Preserving Transformations with "mixing"

Quasi-factors for Infinite-measure Preserving Transformations

This paper is a study of Glasner’s definition of quasi-factors in the setting of infinite-measure preserving system. The existence of a system with zero Krengel entropy and a quasi-factor with positive entropy is obtained. On the other hand, relative zero-entropy for conservative systems implies relative zero-entropy of any quasi-factor with respect to its natural projection onto the factor. Th...

Ergodic and Spectral Analysis of Certain Infinite Measure Preserving Transformations

0. Introduction. Throughout this paper T will denote a measure preserving transformation on a cr-finite infinite measure space (X, (B, m) which is point isomorphic with the Lebesgue measure space of the real line. Unless otherwise stated, T will be one-one. Equations involving functions or sets will always be interpreted modulo sets of measure zero. T is said to be ergodic if T~1E = E, ££(B, im...