A criterion for the approximation of a semicontinuous functional by Lipschitz functionals

V. Ya. Prudnikov, A. G. Podgaev

Pacific National University, Khabarovsk

Abstract: It is proved in [1, 2] that a functional semi-continuous from below and bounded from below in the metric space X is represented as the limit of a non-decreasing family of Lipschitz functionals. In the lemma from [3], a sufficient condition for such a representation is given for a function semi-continuous from below with respect to one of the variables in a finite-dimensional space. This paper contains a criterion for approximation of a semi-continuous functional from below in a metric space by Lipschitz functionals.

Key words: lower semicontinuous functional, metric space.

UDC: 517.965, 517.583

MSC: Primary 39B32; Secondary 33E05

Received: 28.03.2022

DOI: 10.47910/FEMJ202208

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