Compactness and other questions in spaces of uniform measures
Pachl, Jan
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Pachl, Jan
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In this paper we consider two particular classes of supremal functionals defined on Radon measures and we find necessary and sufficient conditions for their lower semicontinuity with respect to the weak* convergence. Some applications to the minimization of functionals defined on BV are presented.
Beloslav Riečan (1974)
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We study the closures of classes of log-concave measures under taking weak limits, linear transformations and tensor products. We investigate which uniform measures on convex bodies can be obtained starting from some class 𝒦. In particular we prove that if one starts from one-dimensional log-concave measures, one obtains no non-trivial uniform mesures on convex bodies.
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