Fatou’s lemma and lower epi-limits of integral functionals. (English) Zbl 1247.28007
Summary: In this work, with the introduction in the \(\sigma \)-finite case of a modulus of equi-integrability, we prove some new extensions of Fatou’s lemma and some of its consequences in the convergence theory of integral functionals. We present the case of a sequence of integral functionals using an analog of Ioffe’s criterion for a sequence of integrands.
MSC:
| 28B20 | Set-valued set functions and measures; integration of set-valued functions; measurable selections |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
References:
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