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Fonction convexe d’une mesure (Convex function of a measure). (French) Zbl 0585.73063
Generalizing some previous works by Temam and co-workers [e.g. R. Temam and F. Demengel, Semin. Goulaouic-Meyer-Schwartz, Equations Deriv. Partielles 1982-1983, Exp. 10, 13 p. (1983; Zbl 0522.28002) and R. Temam, Can. Math. Bull. 25, 392-413 (1982; Zbl 0507.49011)], the author proposes the definition of a convex function of a measure which can be used to formulate mathematical problems in solid mechanics in inhomogeneous materials (e.g., in thermo-elastoplasticity). This is the new point. The local dependence of the resulting bounded Radon measure is studied. The proofs briefly given make use of Radon measure theory and Lebesgue’s decomposition.
Reviewer: G.A.Maugin

74C99 Plastic materials, materials of stress-rate and internal-variable type
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
28A10 Real- or complex-valued set functions
74E05 Inhomogeneity in solid mechanics