值域为B_0空间的抽象囿变函数定义

Definitions of Abstruct Functions of Bounded Variation Having Values in B_0 Space

给出值域为Ｂ０空间的抽象囿变函数的一个定义，并对此种囿变函数进行讨论．其结果是：给出４个此类囿变函数的定义，并相应给出它们之间的等价条件。

Many research works in pseudonormed space B0 have been done from thebook [1] in 1972. But, up to now, research for abstruct functions of boundedvariation having values in B0 space has not been mentioned. We will discuss someproblems of this kind of functions in several papers.In this paper, main results are four definitions of this kind of functions ofbounded variation. We obtained some equivalent conditions in them. Here, x(t) isdefined on [0, 1] and valued in B0 space.