Xin Jian YANG
Let ( Ω,F,μ)
be any complete measurable space, may be infinite measure.In this paper, a sufficient and
necessary condition about the weak compactness of thesets of L1 ( Ω,F,μ) is obtained.
Furtherimore, when be infinite measure, we considerthe sets by sets convergence for finite
generalized measures defined on the measurablespace ( Ω,F) which are absolutely continuous
with and obtained some interestingresults which generalize the Vitali-Hahn-Saks theorem.