ABSTRACT
Various deep interconnections between general topology and measure theory are recognized and widely known at present (see, e.g., [17], [20], [64], [76], [89], [95], [137], [265]). Connections or relationships of such a kind are very fruitful for further development of these two mathematical disciplines. Undoubtedly, the concept of quasi-compactness occupies the central place in general topology and it should be noticed that some direct analogues of this concept can be also met in contemporary measure theory. For instance, it suffices to recall the notion of compact measures first introduced by Marczewski (see [178]). This notion was motivated by concrete problems and questions of measure theory and probability theory. For example, Kolmogorov’s extension theorem from the theory of stochastic processes might be indicated in this context (cf. [17], [20], [26], [199], [265]).
