论文标题
$ \ mathbb {r}^{n} $ in $ \ mathbb中的公元代数的嵌入
Embeddings of metric Boolean algebras in $\mathbb{R}^{N}$
论文作者
论文摘要
配备了（有限加添加的）正概率度量$ m $的布尔代数$ \ a $可以将其变成公制空间$（\ a，d_ {m}）$，其中$ d_ {m}（a，b）= m（（a \ wedge \ neg b）如\ emph {metric boolean代数}。在本文中，我们研究了有限公布代数的原子空间，可以将其嵌入$ \ Mathbb {r}^{n} $（对于特定的$ n $）中。特别是，我们表征了有限代数$ \ a $的正测量的拓扑，以使公制空间$（\ mathsf {at}（\ a），d_m），d_m），d_m）$嵌入在$ \ mathbb {r}^{n} $中。
A Boolean algebra $\A$ equipped with a (finitely-additive) positive probability measure $m$ can be turned into a metric space $(\A , d_{m})$, where $d_{m}(a,b)= m ((a\wedge\neg b)\vee(\neg a\wedge b))$, for any $a,b\in A$, sometimes referred to as \emph{metric Boolean algebra}. In this paper, we study under which conditions the space of atoms of a finite metric Boolean algebra can be isometrically embedded in $\mathbb{R}^{N}$ (for a certain $N$) equipped with the Euclidean metric. In particular, we characterize the topology of the positive measures over a finite algebra $\A$ such that the metric space $(\mathsf{At}(\A), d_m)$ embeds isometrically in $\mathbb{R}^{N}$.
