数学物理学报
數學物理學報
수학물이학보
ACTA MATHEMATICA SCIENTIA
2009年
6期
1518-1522
,共5页
效应代数%态%表示定理.
效應代數%態%錶示定理.
효응대수%태%표시정리.
Effect algebras%States%Representation theorem.
1994年,Foulis和Bennett在表示不可精确测量的量子逻辑结构时引入了效应代数.该文用直接构造的方法,给出一类效应代数上的态表示定理.即,若Ω是紧的Hausdorff拓扑空间,令E(Ω)={f:f∈C(Ω),0 ≤ f ≤ 1),则ψ是(E(Ω),⊕,0,1)上的态当且仅当Ω上存在唯一的正则Borel概率测度μ使得对每个f∈(E(Ω),⊕,0,1),ψ(F)=∫_Ωdμ.
1994年,Foulis和Bennett在錶示不可精確測量的量子邏輯結構時引入瞭效應代數.該文用直接構造的方法,給齣一類效應代數上的態錶示定理.即,若Ω是緊的Hausdorff拓撲空間,令E(Ω)={f:f∈C(Ω),0 ≤ f ≤ 1),則ψ是(E(Ω),⊕,0,1)上的態噹且僅噹Ω上存在唯一的正則Borel概率測度μ使得對每箇f∈(E(Ω),⊕,0,1),ψ(F)=∫_Ωdμ.
1994년,Foulis화Bennett재표시불가정학측량적양자라집결구시인입료효응대수.해문용직접구조적방법,급출일류효응대수상적태표시정리.즉,약Ω시긴적Hausdorff탁복공간,령E(Ω)={f:f∈C(Ω),0 ≤ f ≤ 1),칙ψ시(E(Ω),⊕,0,1)상적태당차부당Ω상존재유일적정칙Borel개솔측도μ사득대매개f∈(E(Ω),⊕,0,1),ψ(F)=∫_Ωdμ.
In 1994, Foulis and Bennett introduced effect algebra to represent the unsharp quantum logic structure. In this paper, using the direct construction method, the authors present a state representation theorem of a class of effect algebras. That is, if Ω is a compact Hausdorff topological space, E(Ω)={f:f∈C(Ω),0 ≤f≤1)}, then ψ is a state of the effect algebra (E(Ω),⊕, 0, 1) if there exists a unique regular Borel probability measure μ on Ω such that for each f∈(E(Ω),⊕,0,1),ψ(F)=∫_Ωdμ.
