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Lecture

Calculus of Variations: Radon-Nikodym Theorem

In course

MATH-604: Some Aspects of Calculus of Variations

The goal of this course is to present an overview on the solvability and the regularity of relevant models of physical, technological and economical systems, which may be formulated as minimization problems of suitable integral functionals. ...

Description

This lecture covers the Radon-Nikodym theorem, which deals with absolutely continuous and penitive functions. It explains the disintegration of measures, the Riesz-Karkov Representation Theorem, and the uniqueness of signed Borel measures. The lecture also discusses the extension of operators, bounded linear transformations, and the essential uniqueness of measures.

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Ontological neighbourhood

Mathematics

Analysis: Functional analysis

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The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations.

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