Banach空间中强可测函数的选择定理

Selection Theorems of Strongly Measurable Functions in Banach Spaces

讨论了Banach空间上强可测函数的选择定理，由此定理得到一个Banach空间自反的充要条件及其它一些有趣的结果。

In this paper, selection theorems for strongly measurable functions in Banach spacesare discussed. The statement: if f(t) is a strongyl measurable fumction from[0, 1 ] to X. (dualspace of Banach space X), then for any 0<ε1, there exists a strongly measurable functicn gε(t) from[0,1] to X such that and (f(t), , a. e. on[0, 1], isexplained, some other interesting results are abtained, whose results have potential usage in theresearch of optimal control problems over Banach spaces.