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lower semicontinuous function

См. также в других словарях:

  • 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

  • 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

  • Spectral theory of ordinary differential equations — In mathematics, the spectral theory of ordinary differential equations is concerned with the determination of the spectrum and eigenfunction expansion associated with a linear ordinary differential equation. In his dissertation Hermann Weyl… …   Wikipedia

  • Bounded variation — In mathematical analysis, a function of bounded variation refers to a real valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense. For a continuous function of a… …   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

  • 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

  • Direct method in the calculus of variations — In the calculus of variations, a topic in mathematics, the direct method is a general method for constructing a proof of the existence of a minimizer for a given functional,[1] introduced by Zaremba and David Hilbert around 1900. The method… …   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

  • Tonelli's theorem (functional analysis) — In mathematics, Tonelli s theorem in functional analysis is a fundamental result on the weak lower semicontinuity of nonlinear functionals on L p spaces. As such, it has major implications for functional analysis and the calculus of variations.… …   Wikipedia

  • Radon measure — In mathematics (specifically, measure theory), a Radon measure, named after Johann Radon, is a measure on the σ algebra of Borel sets of a Hausdorff topological space X that is locally finite and inner regular. Contents 1 Motivation 2 Definitions …   Wikipedia

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