Regular Gleason Measures and Generalized Effect Algebras

TL;DR

This paper investigates various types of measures on quantum logic structures, including regular and sigma-additive measures, and explores their representation within generalized effect algebras.

Contribution

It characterizes conditions under which classes of non-negative measures can be modeled using generalized effect algebras, extending the mathematical framework of quantum measures.

Findings

Identification of conditions for measures to be studied in generalized effect algebras

Analysis of regular and sigma-additive measures on quantum logic

Extension of measure theory in quantum structures

Abstract

We study measures, finitely additive measures, regular measures, and $\sigma$-additive measures that can attain even infinite values on the quantum logic of a Hilbert space. We show when particular classes of non-negative measures can be studied in the frame of generalized effect algebras.