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upper semicontinuous function

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  • Subharmonic function — In mathematics, subharmonic and superharmonic functions are important classes of functions used extensively in partial differential equations, complex analysis and potential theory. Intuitively, subharmonic functions are related to convex… …   Wikipedia

  • semicontinuous — adjective (of a function) That it is continuous almost everywhere, except at certain points at which it is either upper semi continuous or lower semi continuous. See Also: semicontinuity, hemicontinuous …   Wiktionary

  • Multivalued function — This diagram does not represent a true function, because the element 3 in X is associated with two elements, b and c, in Y. In mathematics, a multivalued function (shortly: multifunction, other names: set valued function, set valued map, multi… …   Wikipedia

  • Plurisubharmonic function — In mathematics, plurisubharmonic functions form an important class of functions used in complex analysis. On a Kahler manifold,plurisubharmonic functions form a subset of the subharmonic functions. However, unlikesubharmonic functions (which are… …   Wikipedia

  • Vitali-Carathéodory theorem — noun A theorem which states that any real valued Lebesgue integrable function can be approached arbitrarily closely from below by an upper semicontinuous function and also from above by a lower semicontinuous function …   Wiktionary

  • Compact space — Compactness redirects here. For the concept in first order logic, see compactness theorem. In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness… …   Wikipedia

  • Semi-continuity — For the notion of upper or lower semicontinuous multivalued function see: Hemicontinuity In mathematical analysis, semi continuity (or semicontinuity) is a property of extended real valued functions that is weaker than continuity. A extended real …   Wikipedia

  • Hemicontinuity — In mathematics, the concept of continuity as it is defined for single valued functions is not immediately extendible to multi valued mappings or correspondences. In order to derive a more generalized definition, the dual concepts of upper… …   Wikipedia

  • Kakutani fixed point theorem — In mathematical analysis, the Kakutani fixed point theorem is a fixed point theorem for set valued functions. It provides sufficient conditions for a set valued function defined on a convex, compact subset of a Euclidean space to have a fixed… …   Wikipedia

  • Caristi fixed point theorem — In mathematics, the Caristi fixed point theorem (also known as the Caristi Kirk fixed point theorem) generalizes the Banach fixed point theorem for maps of a complete metric space into itself. Caristi s fixed point theorem is a variation of the… …   Wikipedia

  • Hypograph (mathematics) — In mathematics, the hypograph of a function f : R n → R is the set of points lying on or below its graph:: mbox{hyp} f = { (x, mu) , : , x in mathbb{R}^n,, mu in mathbb{R},, mu le f(x) } subseteq mathbb{R}^{n+1}and the strict hypograph of the… …   Wikipedia

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