超测度空间中预紧性的一个判别法
A Criterion for Precompactness in the Space of Hypermeasures
摘要：
设$Q$表示可分完备空间$X$的Borel $σ$ -代数上的带号测度空间.我们赋予$Q$与规范$\|q\|=\sup|\intϕdq|$，其中的上确界是采取所有Lipschitz与常数1的功能，其模块不超过单位。如果$X$是无限的并且至少有一个极限点，那么这个赋范空间是不完全的。我们称它的完备化为超测度空间。给出了超测度集的预紧性（=相对紧性）的充要条件，它们类似于Prokhorov和Fernique关于测度的定理.
英文摘要：
Let $Q$ denote the space of signed measures on the Borel $σ$-algebra of a separable complete space $X$. We endow $Q$ with the norm $\|q\|=\sup|\intϕdq|$, where the supremum is taken over all Lipschitz with constant 1 functions whose module does not exceed unity. This normed space is incomplete provided $X$ is infinite and has at least one limit point. We call its completion the space of hypermeasures. Necessary and sufficient conditions for precompactness (=relative compactness) of a set of hypermeasures are found. They are similar to those of Prokhorov's and Fernique's theorems for measures.
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