Displaying similar documents to “A weak* approximation of subgradient of convex function”

An isomorphic Dvoretzky's theorem for convex bodies

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 n 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 n satisfying d ( Y K , B 2 k ) C ( 1 + ( k / l n ( n / ( k l n ( n + 1 ) ) ) ) . 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. ...

On some geometric properties concerning closed convex sets.

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.

On mean central limit theorems for stationary sequences

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 𝕃 1 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.