Abstract
Let the quadruple be an invertible abstract dynamical system (see def. 1.1–1.2) and let . In this paper the convex subsets (1.2)–(1.4) of the set M of all finite measures on are examined. We show that if there exists a measurable generator for (see def. 2.2), then the sets (1.2)–(1.4) have extreme points and we determine them (see th. 8.1). As an application we solve some extremal linear problems in the sets (1.2)–(1.4) (see section 9). A curious topological property of the sets of extreme points is given by th. 11.2.
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