Weak sequential convergence in L-1 (mu, X) and an exact version of Fatou's lemma

作者：Khan M Ali^*; Sagara Nobusumi

来源：Journal of Mathematical Analysis and Applications, 2014, 412(1): 554-563.

DOI：10.1016/j.jmaa.2013.10.082

• Fatou's lemma
• Weak convergence
• Bochner integral
• Multifunction
• Saturation property
• Lebesgue property

The class of nonatomic finite measure spaces with the saturation property, as developed in Maharam (1942) and Hoover-Keisler (1984), is characterized by the Fatou (and Lebesgue) property of a well-dominated sequence of multifunctions taking values in a Banach space. With multifunctions reduced to functions, this Fatou characterization also extends to a variant of the closure property found in optimal control theory. The results are developed through a considered overview of the relevant literature on the exact and approximate Fatou lemma phrased in terms of Bochner integration.

• 出版日期2014-4-1