Throughout this paper,let(Ω,ι,μ)be a probability space,D the collection of allleft-continuous distribution functions,and D^+={F(0)=0|F∈D},and L(Ω)the collec-tion of all random variables which is a.s.finite on Ω,and L^+={ξ≥0 a.s.|ξ∈L(Ω)}.For random metric (normed) spaces,see [1]or[2].Theorem 1 Let(M,d)be a complete metric space f:M→M,a contract mappingwith contract coefficient α∈[0,1),L(Ω,m)the collection of all M-valued random vari-
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