ABSTRACT We study observables on a special kind of MV-algebras which are lexicographic MV-algebras, i.e. they are isomorphic to MV-algebras of the form , where is a unital subgroup of and G is a Dedekind σ-complete ℓ-group. Observables are a special kind of σ-homomorphisms defined on the Borel σ-algebra of the real line with values in the lexicographic MV-algebra. They model measurable functions. Spectral resolution is a system of elements of the MV-algebra indexed by real numbers which is monotone, “left continuous”, and going to 0 and 1 if t goes to and to , respectively. The main task of the paper is to show when does a spectral resolution determine an observable x such that for each .

中文翻译：

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词典 MV 代数上的可观察量

摘要 我们研究了一种特殊类型的 MV-代数的可观测量，它们是字典式 MV-代数，即它们同构于形式为 的 MV-代数，其中 是 Observables 是一种特殊的 σ-同态，定义在实线的 Borel σ-代数上，其值在词典 MV-代数中。他们对可测量的函数进行建模。光谱分辨率是由实数索引的 MV 代数元素系统，实数是单调的，“左连续”，如果 t 分别为 和 ，则为 0 和 1。该论文的主要任务是展示光谱分辨率何时确定可观察的 x 使得对于每个 .