一类效应代数的态表示定理

The State Representation Theorem of a Class of Effect Algebras

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φ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),φ(f)=∫_Ωfdμ.

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 φ is a state of the effect algebra （E（Ω）, Ο, 0, 1） if there exists a unique regular Borel probability measure μ on Ω such that for each f （E（Ω）, Ο, 0, 1）, φ （f） = ∫ Ω f dμ.