The Steiner point in infinite dimensions

DOI10.1007/BF02786520zbMath0588.52001MaRDI QIDQ1073341

Richard A. Vitale

Publication date: 1985

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

convex bodyno continuous extension of the Steiner point in infinite dimensions

Mathematics Subject Classification ID

Convex sets without dimension restrictions (aspects of convex geometry) (52A05)

Related Items (16)

Barycentric selectors and a Steiner-type point of a convex body in a Banach space ⋮ Moduli of continuity of selections from nonconvex maps ⋮ A class of bounds for convex bodies in Hilbert space ⋮ On a set-valued Young integral with applications to differential inclusions ⋮ Expected convex hulls, order statistics, and Banach space probabilities ⋮ Covariance identities for normal variables via convex polytopes ⋮ Regularity and integration of set-valued maps represented by generalized Steiner points ⋮ Existence of Weak Solutions to Stochastic Evolution Inclusions ⋮ A maximum principle for differential inclusion problems with state constraints ⋮ Extensions of Lipschitz selections and an application to differential inclusions ⋮ Lipschitz selectors may not yield competitive algorithms for convex body chasing ⋮ A REPRESENTATION OF KEYNES’S LONG-TERM EXPECTATION IN FINANCIAL MARKETS ⋮ Approximations, expansions and univalued representations of multifunctions ⋮ Extended gradient of convex function and capital allocation ⋮ Set-valued extension of operators via Steiner selections. I: Theoretical results. ⋮ Boundary trajectories of systems with unbounded controls

Cites Work

• Uniform neighborhood retracts
• Characterization of the Steiner point
• On nonlinear projections in Banach spaces
• On Steiner points of convex bodies
• Extensions of Lipschitz selections and an application to differential inclusions
• The Lévy-Hinčin representation for random compact convex subsets which are infinitely divisible under Minkowski addition
• Limit theorems for uniform distributions on spheres in high-dimensional euclidean spaces
• Approximation problems for convex polyhedra
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