Abstract theory of uniform distribution
Gilbert Helmberg (1964)
Compositio Mathematica
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Gilbert Helmberg (1964)
Compositio Mathematica
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Gilbert Helmberg (1964)
Compositio Mathematica
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Sergio Falcon, Kishin Sadarangani (2000)
Matematički Vesnik
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Yeneng Sun (1993)
Compositio Mathematica
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A. M. Bruckner, J. G. Ceder, Max Weiss (1966)
Colloquium Mathematicae
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Ivan Niven (1964)
Compositio Mathematica
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J. Cigler (1965-1966)
Compositio Mathematica
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J. Cigler (1971)
Mémoires de la Société Mathématique de France
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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.
Joanna Chachulska (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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Is the Lebesgue measure on [0,1]² a unique product measure on [0,1]² which is transformed again into a product measure on [0,1]² by the mapping ψ(x,y) = (x,(x+y)mod 1))? Here a somewhat stronger version of this problem in a probabilistic framework is answered. It is shown that for independent and identically distributed random variables X and Y constancy of the conditional expectations of X+Y-I(X+Y > 1) and its square given X identifies uniform distribution either absolutely continuous...
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.