%0 Journal Article
%T Some Observations on Dirac Measure-Preserving Transformations and their Results
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Alijani, Azadeh
%A Nazari, Zohreh
%D 2019
%\ 04/01/2019
%V 14
%N 1
%P 117-126
%! Some Observations on Dirac Measure-Preserving Transformations and their Results
%K Dirac measure
%K Measure algebra
%K Measure-preserving transformation
%R 10.22130/scma.2018.61771.226
%X 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.
%U https://scma.maragheh.ac.ir/article_34485_8c88bf3e36a3286401cca14068f4ff4c.pdf