L^p(Ω,X)中可分解集的性质

Property of decomposable sets in L^p(Ω,X)

研究了函数空间Lp(Ω,X)(1≤p≤∞)中可分解集的性质,得出了当1≤p≤∞时含有内点的可分解集在Lp(Ω,X)中稠密;并给出了类似于凸集的Mazur定理的关于可分解集的收敛定理。

The property of decomposable sets in LP（Ω9,X）（1 ≤p ≤∞） is discussed in this paper. It must be dense in the whole space when it has an inner point in Lp （Ω,X）（1 ≤p ≤∞ ）. The convergence theorem of decomposable sets similar to Mazur theorem is proved.