论文标题
措施和国家的正交性
Orthogonality of measures and states
论文作者
论文摘要
由于Preiss和Rataj，我们给出了该定理的简短证明，表明在波兰空间上没有骨概率测量的最大分析性正交家族（MOF）。当基础空间紧凑而完美时，我们证明了非最大程度的见证人的一组是稳定的。我们的论点基于Preiss和Rataj的原始证明，但进行了重大简化。证明一般证明，在$ \ mathsf {ma} + \ neg \ neg \ neg \ neg \ neg \ mathsf {ch} $下没有$ \ mathbf {σ^1_2} $ mofs，在$ \ mathsf {pd} $下，没有投影mofs，没有$ \ mathsf {adsf {ad ad aD} $ afs af。我们还概括了由于Kechris和Sofronidis引起的结果，并指出，对于每个分析性的Borel概率指标的分析性家族，都有与家族中所有措施的产品量度措施，都可以与一定类别的C*-Algebras的州有关。
We give a short proof of the theorem due to Preiss and Rataj stating that there are no analytic maximal orthogonal families (mofs) of Borel probability measures on a Polish space. When the underlying space is compact and perfect, we show that the set of witnesses to non-maximality is comeagre. Our argument is based on the original proof by Preiss and Rataj, but with significant simplifications. The proof generalises to show that under $\mathsf{MA} + \neg \mathsf{CH}$ there are no $\mathbf{Σ^1_2}$ mofs, that under $\mathsf{PD}$ there are no projective mofs and that under $\mathsf{AD}$ there are no mofs at all. We also generalise a result due to Kechris and Sofronidis, stating that for every analytic orthogonal family of Borel probability measures there is a product measure orthogonal to all measures in the family, to states on a certain class of C*-algebras.
