Abstract
In this chapter we continue our investigations on the applications of rigid, BTm-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],<,BTm and make use of the complete groupoid BTm = ([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 BTm-valued topological spaces and the application of the principle of continuous extension to BTm -valued continuous maps. In this context we also touch the question to what extent rigid BTm -valued topologies form an enrichment of traditional general topology.
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© 2001 Springer Science+Business Media New York
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Höhle, U. (2001). Probability Measures. In: Many Valued Topology and its Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1617-0_10
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DOI: https://doi.org/10.1007/978-1-4615-1617-0_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5643-1
Online ISBN: 978-1-4615-1617-0
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