标题： 不可表示的量子测度 显示英文标题

标题： Non-representable quantum measures

摘要： 等级-$d$在集合$X$上的$\sigma$-代数$\mathcal{A}\subseteq 2^X$是满足在量子力学中最初作为干扰算子引入的一系列弱可加性条件之一的测度的推广。 每个带符号的多测度$\lambda$在$(X,\mathcal{A})^d$上产生一个等级为$d$的测度作为其对角线$\widetilde{\lambda}(A):=\lambda(A,\cdots,A)$，并且我们证明一旦$d\ge 2$测度（与多测度相反）不足以满足要求：一个$\lambda$产生$\mu=\widetilde{\lambda}$的单独$\sigma$-可加性通常无法增强为全局$\sigma$-可加性。 这修改了文献中的一个结果，在$d=2$的情况下断言相反的情况。 显示英文摘要

摘要： Grade-$d$ measures on a $\sigma$-algebra $\mathcal{A}\subseteq 2^X$ over a set $X$ are generalizations of measures satisfying one of a hierarchy of weak additivity-type conditions initially introduced as interference operators in quantum mechanics. Every signed polymeasure $\lambda$ on $(X,\mathcal{A})^d$ produces a grade-$d$ measure as its diagonal $\widetilde{\lambda}(A):=\lambda(A,\cdots,A)$, and we prove that as soon as $d\ge 2$ measures (as opposed to polymeasures) do not suffice: the separate $\sigma$-additivity of a $\lambda$ producing $\mu=\widetilde{\lambda}$ cannot, generally, be amplified to global $\sigma$-additivity. This amends a result in the literature, asserting the contrary in case $d=2$.