Rigidity of smooth one-sided Bernoulli endomorphisms.
Bruin, Henk, Hawkins, Jane (2009)
The New York Journal of Mathematics [electronic only]
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Bruin, Henk, Hawkins, Jane (2009)
The New York Journal of Mathematics [electronic only]
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Ethan Akin, Randall Dougherty, R. Daniel Mauldin, Andrew Yingst (2008)
Colloquium Mathematicae
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For measures on a Cantor space, the demand that the measure be "good" is a useful homogeneity condition. We examine the question of when a Bernoulli measure on the sequence space for an alphabet of size n is good. Complete answers are given for the n = 2 cases and the rational cases. Partial results are obtained for the general cases.
Barnes, Julia A., Koss, Lorelei (2000)
International Journal of Mathematics and Mathematical Sciences
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Jenkins, Russell S., Garimella, Ramesh V. (2000)
International Journal of Mathematics and Mathematical Sciences
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Ricardo Faro Rivas, Juan A. Navarro, Juan Sancho (1994)
Extracta Mathematicae
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Kim, Jeong H. (1995)
International Journal of Mathematics and Mathematical Sciences
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Schaerf, H.M. (1949)
Portugaliae mathematica
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Noboru Endou (2017)
Formalized Mathematics
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The purpose of this article is to show Fubini’s theorem on measure [16], [4], [7], [15], [18]. Some theorems have the possibility of slight generalization, but we have priority to avoid the complexity of the description. First of all, for the product measure constructed in [14], we show some theorems. Then we introduce the section which plays an important role in Fubini’s theorem, and prove the relevant proposition. Finally we show Fubini’s theorem on measure.
Robert Morris Pierce
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Noboru Endou (2016)
Formalized Mathematics
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In this article we formalize in Mizar [5] product pre-measure on product sets of measurable sets. Although there are some approaches to construct product measure [22], [6], [9], [21], [25], we start it from σ-measure because existence of σ-measure on any semialgebras has been proved in [15]. In this approach, we use some theorems for integrals.
Eigen, S.J., Prasad, V.S. (1997)
The New York Journal of Mathematics [electronic only]
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A. Ülger (2007)
Studia Mathematica
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Let G be a locally compact abelian group and M(G) its measure algebra. Two measures μ and λ are said to be equivalent if there exists an invertible measure ϖ such that ϖ*μ = λ. The main result of this note is the following: A measure μ is invertible iff |μ̂| ≥ ε on Ĝ for some ε > 0 and μ is equivalent to a measure λ of the form λ = a + θ, where a ∈ L¹(G) and θ ∈ M(G) is an idempotent measure.
Piotr Zakrzewski (1997)
Colloquium Mathematicae
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Let G be a group of homeomorphisms of a nondiscrete, locally compact, σ-compact topological space X and suppose that a Haar measure on X exists: a regular Borel measure μ, positive on nonempty open sets, finite on compact sets and invariant under the homeomorphisms from G. Under some mild assumptions on G and X we prove that the measure completion of μ is the unique, up to a constant factor, nonzero, σ-finite, G-invariant measure defined on its domain iff μ is ergodic and the G-orbits...