Sharapov V.G. Measurable partitions generated by quasiendomorphismes of Lebesgue space
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Sharapov Viktor Georgievich
Candidate of Physics and Mathematics, Associate Professor, Department of Fundamental Information Science and Optimal Control, Volgograd State University
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
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.
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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