@article {
author = {Alijani, Azadeh and Nazari, Zohreh},
title = {Some Observations on Dirac Measure-Preserving Transformations and their Results},
journal = {Sahand Communications in Mathematical Analysis},
volume = {14},
number = {1},
pages = {117-126},
year = {2019},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2018.61771.226},
abstract = {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.},
keywords = {Dirac measure,Measure algebra,Measure-preserving transformation},
url = {https://scma.maragheh.ac.ir/article_34485.html},
eprint = {https://scma.maragheh.ac.ir/article_34485_8c88bf3e36a3286401cca14068f4ff4c.pdf}
}