Some Observations on Dirac Measure-Preserving Transformations and their Results
Publish Year: 1398
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_SCMA-14-1_010
تاریخ نمایه سازی: 18 تیر 1398
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.
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Authors
Azadeh Alijani
Vali-e-Asr University of Rafsanjan, Department of Mathematics, P. O. Box ۷۷۱۳۹۳۶۴۱۷, Rafsanjan, Iran.
Zohreh Nazari
Vali-e-Asr University of Rafsanjan, Department of Mathematics, P. O. Box ۷۷۱۳۹۳۶۴۱۷, Rafsanjan, Iran.
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