Probability Measures

Abstract

In this chapter we continue our investigations on the applications of rigid, B_Tm-valued topologies to the field of probability measures which we have initiated in a sequence of examples in Chapter 6 (cf. 6.1.5, 6.2.2.3, 6.3.2.5 and 6.4.2.9), Therefore we view the real interval as complete MV-algebra J= ([0, l],<,B_Tm and make use of the complete groupoid B_Tm = ([0, l],<, ⊞) where ⊞ denotes the arithmetic mean (cf. Example 4.1.9(b)). The main subject of this chapter consists in the compactification of certain, rigid B_Tm-valued topological spaces and the application of the principle of continuous extension to B_Tm -valued continuous maps. In this context we also touch the question to what extent rigid B_Tm -valued topologies form an enrichment of traditional general topology.