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Some Observations on Dirac Measure-Preserving Transformations and their Results

Journal: Sahand Communications in Mathematical Analysis (Vol.14, No. 1)

Publication Date:

Authors : ; ;

Page : 117-126

Keywords : Dirac measure; Measure algebra; Measure-preserving transformation;

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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 measure space and its measure algebras are presented. Then all of measure spaces that are isomorphic with a Dirac measure space are characterized and the concept of a Dirac measure class is introduced and its elements are characterized. More precisely, it is shown that every absolutely continuous measure with respect to a Dirac measure belongs to the Dirac measure class. Finally, the relation between Dirac measure preserving transformations and strong-mixing is studied.

Last modified: 2019-04-28 14:13:45