TY - JOUR
ID - 34485
TI - Some Observations on Dirac Measure-Preserving Transformations and their Results
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Alijani, Azadeh
AU - Nazari, Zohreh
AD - Vali-e-Asr University of Rafsanjan, Department of Mathematics, P. O. Box 7713936417, Rafsanjan, Iran.
Y1 - 2019
PY - 2019
VL - 14
IS - 1
SP - 117
EP - 126
KW - Dirac measure
KW - Measure algebra
KW - Measure-preserving transformation
DO - 10.22130/scma.2018.61771.226
N2 - 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.
UR - https://scma.maragheh.ac.ir/article_34485.html
L1 - https://scma.maragheh.ac.ir/article_34485_8c88bf3e36a3286401cca14068f4ff4c.pdf
ER -