局部凸空间上矢值测度某些有界变差的等价性

The Equivalent Properties About Vector Measures of Various Bounded Variation with Valued in Locally Convex Spaces

讨论了局部凸空间上矢值测度的某些有界交差的等价关系，主要结果是当Ｘ为半核桶空间时，矢位测度产Ｆ：→Ｘ关于弱有界变差，有界半变差，Ｈ－有界变差及有界变差是等价的．

The equivalent properties about vector measures of various variation with valued in locally convex spaces are investigated, the obtained major result is that when X is a semi kernel barreled space, a vector measure F from a field of subsets of a set Ω to the space X, the following conditions are equivalent.(i) F is weakly bounded variation.(ii) F is bounded semivariation.(iii) F is H-bounded variation.(iv) F is bounded variation.