Displaying similar documents to “An Alpern tower independent of a given partition”

Partition sensitivity for measurable maps

C. A. Morales (2013)

Mathematica Bohemica

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We study countable partitions for measurable maps on measure spaces such that, for every point x , the set of points with the same itinerary as that of x is negligible. We prove in nonatomic probability spaces that every strong generator (Parry, W., Aperiodic transformations and generators, J. London Math. Soc. 43 (1968), 191–194) satisfies this property (but not conversely). In addition, measurable maps carrying partitions with this property are aperiodic and their corresponding spaces...

On restricted measurability

A. K. Mookhopadhyaya (1966)

Annales de l'institut Fourier

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Dans cet article, on étudie, certains résultats sur la mesurabilité restreinte [Trevor J. Mc Minn, Restricted Measurability, (1948), vol. 54, July-Dec., 1105] et à l’aide de cette notion, on construit une mesure de Radon analogue à celle de Mr. Sion [A Characterization of weak convergence, (1964), vol. 14, no 3, 1059] et on établit certaines de ses propriétés.

Generalized interval exchanges and the 2–3 conjecture

Shmuel Friedland, Benjamin Weiss (2005)

Open Mathematics

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We introduce the notion of a generalized interval exchange φ 𝒜 induced by a measurable k-partition 𝒜 = A 1 , . . . , A k of [0,1). φ 𝒜 can be viewed as the corresponding restriction of a nondecreasing function f 𝒜 on ℝ with f 𝒜 ( 0 ) = 0 , f 𝒜 ( k ) = 1 . A is called λ-dense if λ(A i∩(a, b))>0 for each i and any 0≤ a< b≤1. We show that the 2–3 Furstenberg conjecture is invalid if and only if there are 2 and 3 λ-dense partitions A and B of [0,1), such that f 𝒜 ∘ f ℬ = f ℬ ∘ f 𝒜 . We give necessary and sufficient conditions for this equality to hold. We...

The Relevance of Measure and Probability, and Definition of Completeness of Probability

Bo Zhang, Hiroshi Yamazaki, Yatsuka Nakamura (2006)

Formalized Mathematics

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In this article, we first discuss the relation between measure defined using extended real numbers and probability defined using real numbers. Further, we define completeness of probability, and its completion method, and also show that they coincide with those of measure.