Some Observations on Dirac Measure-Preserving Transformations and their Results

Sahand Communications in Mathematical Analysis

Zohreh Nazari¹  Azadeh Alijani¹ 

[1] Vali-e-Asr University of Rafsanjan, Department of Mathematics, P. O. Box 7713936417, Rafsanjan, Iran.;

关键词: Dirac measure;    Measure algebra;    Measure-preserving transformation;   

DOI  :  10.22130/scma.2018.61771.226

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown