Brooks-Jewett and Nikodym convergence theorems for orthoalgebras that have the weak subsequential interpolation property

Abstract

A weak form of σ-orthocompleteness or σ-orthosummability, referred to as the Weak Subsequential Interpolation Property, is defined for Orthoalgebras. It is shown that the class of Orthoalgebras that have this property properly contains the class of σ-orthoalgebras. The Brooks-Jewett theorem and the Nikodym convergence theorem for semigroup-valued finitely additive and s-bounded measures defined on an orthoalgebra satisfying the Weak Subsequential Interpolation Property are proved.