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- W1978214844 abstract "Let I = [0, 1], :13 = Lebesgue measurable subsets of [0, 1], and let A denote the Lebesgue measure on (I, 'I13). Let T: I -* I be measurable and surjective. We say T is full, if for all A E 93, A(A) > 0, T(A), T 2(A), . . ., measurable, the condition (1) lim AX(T(A)) = 1 holds. We say T is interval full if (1) holds for any interval A c I. In this note, we give an example of T: I -+ I which is continuous and interval full, but not full. We also show that for a class of transformations T satisfying Renyi's condition, interval fullness implies fullness. Finally, we show that fullness is not preserved under limits on the surjections." @default.
- W1978214844 created "2016-06-24" @default.
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- W1978214844 date "1982-02-01" @default.
- W1978214844 modified "2023-09-25" @default.
- W1978214844 title "On the fullness of surjective maps of an interval" @default.
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- W1978214844 doi "https://doi.org/10.1090/s0002-9947-1982-0637701-x" @default.
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