k分Cantor集C_k上p方可积函数空间L^P(C_k,μ)的可分性

The Separability of L^P(C_k,μ)

文献[1]已知三分Cantor集C上p方可积函数空间LP(C,μ)(1≤p<∞)是可分的,将此结论推广到k分Cantor集Ck(k为>1的奇数)上,证明了k分Cantor集Ck上p方可积函数空间LP(Ck,μ)(1≤p<∞)也是可分的.

According to the bibliography[1],it is known that the space L^P（C,μ）（1≤p∞） is separable.This conclusion has been generalized to the kth Cantor sets Ck （in which k is an odd integer larger than one）,and it is proved that the space LP（Ck,μ）（1≤p∞） is separable,too.