关于集值测度的性质

On the Properties of Set-valued Measures

本文首先建立了集值情况的 Orlicz-Pettis 定理,从而解决了集值测度的强可加问题,集值集函数弱可列可加的充要条件;在集值测度σ-有界变差的条件下给出集值测度的凸性定理;对一般集值测度得到集值测度的选择定理;并且讨论了集值测度值域的紧性、弱紧性定理.

This thesis set up Orlicz-Pettis theorem under set-valued condition for the first time, thus solved the problem of strong additive problem of set-valued measurement and the suf- ficient and necessary condition of weak countable and additive of set-valued set function; provided the convex theorem of set-valued measurement under the condition of set-valued measurement σ-bounded variation;obtained selection theorem of set-valued measurement to normal set-valued measurement;the compact weak compact theorem of the value ralue range of set-valued measurement were also discussed here.