【摘要】 证明了(Ω,Σ)上的任一有限可加测度μ可保变差的延拓为(Ω,2Ω)上一有限可加测度,满足‖‖=‖μ‖且|Σ=μ.作为它的应用,可得到:m*(s)=sμu∈pUμ(s),m*(s)=μi∈nfUμ(s),其中U={μ∈F+},μ为λ的保变差延拓,λ为([0,1],蒡)上的Lebesgue测度.更多还原

【Abstract】 This paper shows that each finitely additive measures μ on(Ω,Σ) can be variation-persevered extension to finitely additive measure  on(Ω,2Ω),satisfying ‖‖=‖μ‖ and|Σ=μ.As its application,it also proves that m*(s)=sμu∈pU μ(s),m*(s)=iμn∈fU μ(s),which U={μ∈F+},μ is variation-persevered extended of λ andλ is Lebesgue measure on([0,1],Σ).更多还原