Sharapov V.G. Measurable partitions generated by quasiendomorphismes of Lebesgue space

Sharapov Viktor Georgievich
 
Candidate of Physics and Mathematics, Associate Professor, Department of Fundamental Information Science and Optimal Control, Volgograd State University
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Prospekt Universitetskij, 100, 400062 Volgograd, Russian Federation
 
Abstract. In the paper a class of measurable partitions ξ of Lebesque space M with conditional measures µξ(C)>0, C ∈ ξ, not necessarily µξ(C)=1 as by V.A. Rokhlin, but if M/ξ = [0,1], g(x)=µξ(Cx), 0∫1g(x)dx=1, is considered.
It is shown that for which such partition it exists quasiendomorphism T, for which 
T−1ε=ξ, ε — pointwise partition.
 
Key words: measurable partitions, quasiendomorphisms.

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Measurable partitions generated by quasiendomorphismes of Lebesgue space by Sharapov V.G. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. Issue 13 2010 pp. 75-79
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