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A selection lemma for sequences of measurable sets, and lower semicontinuity of multiple integrals. (English) Zbl 0404.28004

MSC:
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
49J99 Existence theories in calculus of variations and optimal control
46G05 Derivatives of functions in infinite-dimensional spaces
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References:
[1] BACHMAN-NARICI: Functional Analysis. Academic Press, New York 1966
[2] BERKOVITZ, L.D.: Lower Semicontinuity of Integral Functionals. Transaction of the American Mathematical Society, 192 (1974), pp. 51-57 · Zbl 0294.49001
[3] CESARI, L.: A Necessary and Sufficient Condition for Lower Semicontinuity. BAMS, 80 (1974), pp. 467-472 · Zbl 0287.49003
[4] CESARI, L.: Lower Semicontinuity and Lower Closure Theorems. Annali di Math. 98 (1974), pp. 381-397 · Zbl 0281.49006
[5] FEDERER, H.: Geometric Measure Theory. Springer Berlin-Heidelberg-New York 1969 · Zbl 0176.00801
[6] HALMOS, P.R.: Measure Theory. Springer, Berlin-Heidelberg-New York 1966
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