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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A sufficient condition for the lower semicontinuity of parametric integrals


Author: Edward Silverman
Journal: Trans. Amer. Math. Soc. 167 (1972), 465-469
MSC: Primary 49A50; Secondary 28A75
MathSciNet review: 0296785
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Abstract: We use simple convex functions and standard techniques in area theory to treat Morrey's extension of McShane's lower semicontinuity theorem for parametric integrals. This enables us to eliminate some technical hypotheses, simplify the proof and obtain a more general result.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0296785-5
PII: S 0002-9947(1972)0296785-5
Keywords: Simple area, parametric integral
Article copyright: © Copyright 1972 American Mathematical Society