Orthoalgebras and Noncommutative Measure Theory.
Abstract
Notions of orthosummability and sigma orthosummability are defined for orthoalgebras. It is shown that these notions extend the known notions of orthocompleteness and sigmaorthocompleteness for orthomodular posets and that the class of orthosummable (respectively, sigmaorthosummable) orthoalgebras properly contains the class of orthocomplete (respectively, sigmaorthocomplete) orthomodular posets. Characterizations of these orthoalgebras as well as orthocomplete orthomodular posets in terms of their chains are given. Also, a weak form of sigma orthosummability, referred to as Weak Subsequential Interpolation Property, is defined for orthoalgebras; and it is shown that this latter class of orthoalgebras properly contains the former class of sigmaorthosummable orthoalgebras (called sigmaorthoalgebras). The BrooksJewett Theorem, the Nikodym Convergence Theorem and the NikodymVitaliHahnSaks Theorem for semigroup valued functions defined on a sigma orthoalgebra (respectively, an orthoalgebra satisfying the Weak Subsequential Interpolation Property) are proved.
 Publication:

Ph.D. Thesis
 Pub Date:
 1993
 Bibcode:
 1993PhDT.......145H
 Keywords:

 Mathematics; Physics: General; Statistics