Noise as a Boolean algebra of sigma-fields. II. Classicality, blackness, spectrum

TL;DR

This paper explores the structure of noises and Boolean algebras of sigma-fields, focusing on classicality, blackness, and spectral analysis to deepen understanding of their mathematical properties.

Contribution

It introduces a framework connecting noises with Boolean algebras of sigma-fields and utilizes spectral sets to analyze their properties.

Findings

Boolean algebras of sigma-fields can be black, similar to noises

Spectral sets are effective tools in this framework

A noise can be viewed as a homomorphism between Boolean algebras

Abstract

Similarly to noises, Boolean algebras of sigma-fields can be black. A noise may be treated as a homomorphism from a Boolean algebra of regular open sets to a Boolean algebra of sigma-fields. Spectral sets are useful also in this framework.