A Simple Proof of the Majorizing Measure Theorem.
M. Talagrand (1992)
Geometric and functional analysis
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M. Talagrand (1992)
Geometric and functional analysis
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Arturo Erdely (2017)
Kybernetika
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A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the proposed dependence measure based on the empirical subcopula is provided, along with an R package to perform the corresponding calculations.
Milan Merkle, Liljana Petrovic (1997)
Aequationes mathematicae
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C. Olech (1967)
Colloquium Mathematicae
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Helge Tverberg (2012)
Acta Arithmetica
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S. Kwapien (1972-1973)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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Jan Rosiński (1975)
Colloquium Mathematicae
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Robert E. Zink (1966)
Colloquium Mathematicae
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Robert Morris Pierce
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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.
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.
D. Caponetti, G. Trombetta (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let X be an infinite-dimensional Banach space. The measure of solvability ν(I) of the identity operator I is equal to 1.
Huixue Lao (2008)
Acta Arithmetica
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T. Świątkowski (1967)
Colloquium Mathematicae
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Marcin Lis (2012)
Bulletin of the Polish Academy of Sciences. Mathematics
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We continue the research of Latała on improving estimates of the pth moments of sums of independent random variables with logarithmically concave tails. We generalize some of his results in the case of 2 ≤ p ≤ 4 and present a combinatorial approach for even moments.
Czesław Stępniak (2015)
Discussiones Mathematicae Probability and Statistics
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Correlation coefficient is a well known measure of (linear) dependence between random variables. In his textbook published in 1980 L.T. Kubik introduced an analogue of such measure for random events A and B and studied its basic properties. We reveal that this measure reduces to the usual correlation coefficient between the indicator functions of A and B. In consequence the resuts by Kubik are obtained and strenghted directly. This is essential because the textbook is recommended by...