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The Minlos lemma for positive-definite functions on additive subgroups of ℝ n

W. Banaszczyk (1997)

Studia Mathematica

Let H be a real Hilbert space. It is well known that a positive-definite function φ on H is the Fourier transform of a Radon measure on the dual space if (and only if) φ is continuous in the Sazonov topology (resp. the Gross topology) on H. Let G be an additive subgroup of H and let G p c ∧ (resp. G b ∧ ) be the character group endowed with the topology of uniform convergence on precompact (resp. bounded) subsets of G. It is proved that if a positive-definite function φ on G is continuous in the Gross topology,...

The Poulsen simplex

Joram Lindenstrauss, Gunnar Olsen, Y. Sternfeld (1978)

Annales de l'institut Fourier

It is proved that there is a unique metrizable simplex S whose extreme points are dense. This simplex is homogeneous in the sense that for every 2 affinely homeomorphic faces F 1 and F 2 there is an automorphism of S which maps F 1 onto F 2 . Every metrizable simplex is affinely homeomorphic to a face of S . The set of extreme points of S is homeomorphic to the Hilbert space ℓ 2 . The matrices which represent A ( S ) are characterized.

The skeleta of convex bodies

David G. Larman (2009)

Banach Center Publications

The connectivity and measure theoretic properties of the skeleta of convex bodies in Euclidean space are discussed, together with some long standing problems and recent results.

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