Measurable partitions generated by quasiendomorphismes

In the paper a class of measurable partitions ƒ of Lebesque space M with conditional measures ƒƒ(C) > 0, C ¶ ƒ, not necessarily ƒƒ(C) = 1 as by V.A. Rokhlin, but if M/ƒ = [0, 1], g(x) = ƒƒ(Cx), 1 R0 g(x)dx = 1, is considered. It is shown that for which such partition it exists quasiendomorphism T, for which T−1ƒ = ƒ, ƒ - pointwise partition.