Theory of Probability &Its Applications, Volume 64, Issue 4, Page 615-630, January 2020.
This paper describes Fatou's lemma for a sequence of measures converging weakly to a finite measure and for a sequence of functions whose negative parts are uniformly integrable with respect to these measures. The paper also provides new formulations of uniform Fatou's lemma, uniform Lebesgue's convergence theorem, the Dunford--Pettis theorem, and the fundamental theorem for Young measures based on the equivalence of uniform integrability and the apparently weaker property of asymptotic uniform integrability for sequences of functions and finite measures.

中文翻译：

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一致可积性条件下法头微弱对策的引理

概率论及其应用，第64卷，第4期，第615-630页，2020年1月。
本文描述了Fatou的引理，即一系列测度弱收敛到有限测度，以及一系列函数的负部分相对于一致可积这些措施。本文还根据统一可积性的等价性和函数序列的渐近统一可积性的较弱特性，提供了统一的法头引理，统一的Lebesgue收敛定理，邓福德-佩蒂斯定理以及Young测度的基本定理的新表述。和有限的措施。