p－Banach空间中的级数与囿变函数

ON SERIES AND BOUNDED VARIATION FUNCTIONS IN p -BANACH SPACES

证明了赋ｐ－范向量空间Ｘ完备当且仅当其中的绝对收敛级数必收敛；

It is proved that p -normed vector space X is complete if and only if absolutely convergent series is convergent,and that in p -Banach spaces,abstract function's bounded variation is equivalent with its p -weakly bounded variation if and only if series's absolutely convergent is equivalent with its p -weakly absolufely convergent.