Convergence Theorems for Lattice Group-Valued Measures

Convergence Theorems for Lattice Group-Valued Measures

Convergence Theorems for Lattice Group-valued Measures explains limit and boundedness theorems for measures taking values in abstract structures. The book begins with a historical survey about these ...
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Appendix

Pp. 499-508 (10)

Antonio Boccuto and Xenofon Dimitriou

Abstract

We present an abstract approach on probability measures, events and random variables, involving in particular lattice theory, distance functions, σ-additive extensions of finitely additive functions, some kinds of convergences in the lattice setting, which can be considered even in more abstract contexts. Furthermore we pose some open problems.

Keywords:

Almost uniform convergence, attribute, Boolean algebra, Boolean σ- algebra, concept, distance function, duality principle, experiment, finitely additive function, lattice, normalized distance, object, order convergence, probability, random variable, regular lattice, subsemilattice, supersemilattice, σ-additive function, σ-regular lattice.

Affiliation:

Dipartimento di Matematica e Informatica via Vanvitelli, 1 I-06123 Perugia Italy.