An elementary proof of an equivalence theorem relevant in the theory of optimization

DOI10.1007/BF00938425zbMath0536.46018OpenAlexW4241543037MaRDI QIDQ5896293

Patrizia Pucci, Lamberto Cesari

Publication date: 1985

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00938425

zbMATH Keywords

Lebesgue integrationLusin's theoremequiabsolute integrabilityAscoli's theoremDunford-Pettis conditionequiabsolute continuityNagumo functionsweak convergence in \(L_ 1\)weak relative compactness in \(L_ 1\)

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Integration with respect to measures and other set functions (28A25) Existence theories for problems in abstract spaces (49J27) Compactness in topological linear spaces; angelic spaces, etc. (46A50)

Cites Work

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• Optimal strategies for seeking information. Models for statistics, choice reaction times, and human information processing
• Variation, Multiplicity, and Semicontinuity
• An existence theorem for pareto problems

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