Consider an ‘experiment' which can be repeated indefinitely often resulting in independent random outcomes. Fix attention on a finite number of possible (sets of) outcomes E1, E2, … and define W = W(N1, N2, …) to be the expected number of repetitions needed to ensure that E1 has occurred (at least) N1 times, E2 has occurred (at least) N2 times, etc. This article examines the asymptotic behavior of W as a function of the sum ΣjNj, as the latter grows without bound.

An abelian topological group can be considered simply as an abelian group or as a topological space. The question considered in this article is whether the topological group structure is determined by these weaker structures. Denote homeomorphism, isomorphism, and homeomorphic isomorphism by ≈, ≅ , and =, respectively. The principal results are these.

Theorem 1. If G 1andG 2are locally compact and connected, then G 1≈ G 2implies G 1= G 2.

The growth of the United States' economic influence in twentieth-century Canada was intimately related to the continuation of the “National Policy” of protectionist tariffs. Professor Scheinberg argues that Canadians initially welcomed America's consciously expansionist thrust, and that they eventually became entangled in the problems of seeking rapid economic growth along with economic independence from both the older imperialism of Great Britain and the newer variety represented by the United States.