On a.e. convergence of expansion with respect to a bounded orthonormal system of polygonals
F. Schipp (1976)
Studia Mathematica
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F. Schipp (1976)
Studia Mathematica
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Carsten Schütt (1982)
Studia Mathematica
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Y. Gordon, O. Guédon, M. Meyer (1998)
Studia Mathematica
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We prove that there exist constants C>0 and 0 < λ < 1 so that for all convex bodies K in with non-empty interior and all integers k so that 1 ≤ k ≤ λn/ln(n+1), there exists a k-dimensional affine subspace Y of satisfying . This formulation of Dvoretzky’s theorem for large dimensional sections is a generalization with a new proof of the result due to Milman and Schechtman for centrally symmetric convex bodies. A sharper estimate holds for the n-dimensional simplex. ...
Carsten Schütt (1982)
Compositio Mathematica
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Gerhard Larcher (1988)
Acta Arithmetica
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D. N. Kutzarova, Pei-Kee Lin, P. L. Papini, Xin Tai Yu (1991)
Collectanea Mathematica
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In this article, we consider the (weak) drop property, weak property (a), and property (w) for closed convex sets. Here we give some relations between those properties. Particularly, we prove that C has (weak) property (a) if and only if the subdifferential mapping of Cº is (n-n) (respectively, (n-w)) upper semicontinuous and (weak) compact valued. This gives an extension of a theorem of Giles and the first author.
H. Benabdellah, C. Castaing (1997)
Collectanea Mathematica
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Françoise Lust-Piquard, Walter Schachermayer (1989)
Studia Mathematica
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Jérôme Dedecker, Emmanuel Rio (2008)
Annales de l'I.H.P. Probabilités et statistiques
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In this paper, we give estimates of the minimal distance between the distribution of the normalized partial sum and the limiting gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.