Non-uniform integrability and generalized Young measures.
Alibert, J.J., Bouchitté, G. (1997)
Journal of Convex Analysis
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Alibert, J.J., Bouchitté, G. (1997)
Journal of Convex Analysis
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M. Łachwa (1977)
Colloquium Mathematicae
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Kenny Koffi Siggini (2009)
Colloquium Mathematicae
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We prove criteria for relative compactness in the space of set-valued measures whose values are compact convex sets in a Banach space, and we generalize to set-valued measures the famous theorem of Dieudonné on convergence of real non-negative regular measures.
Jan K. Pachl (1979)
Colloquium Mathematicae
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K. Musiał (1973)
Colloquium Mathematicae
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Mikhail A. Sychev (2000)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Beloslav Riečan (1974)
Časopis pro pěstování matematiky
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Omar Anza Hafsa, Jean-Philippe Mandallena, Gérard Michaille (2005)
ESAIM: Control, Optimisation and Calculus of Variations
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Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the -limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.
Artur Bartoszewicz (1978)
Colloquium Mathematicae
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Flemming Topsoe (1969)
Mathematica Scandinavica
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Matthew Badger, Raanan Schul (2017)
Analysis and Geometry in Metric Spaces
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A measure is 1-rectifiable if there is a countable union of finite length curves whose complement has zero measure. We characterize 1-rectifiable Radon measures μ in n-dimensional Euclidean space for all n ≥ 2 in terms of positivity of the lower density and finiteness of a geometric square function, which loosely speaking, records in an L2 gauge the extent to which μ admits approximate tangent lines, or has rapidly growing density ratios, along its support. In contrast with the classical...
Jantas, Alicja (2015-11-10T12:04:38Z)
Acta Universitatis Lodziensis. Folia Mathematica
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