On F-Atoms and μ-Atoms of a Measure Space, and Atoms of Derived σ-Algebras

Abstract

This study explores the concepts of ℱ-atoms and μ-atoms within a measure space and examines their interrelationship. Conditions are identified under which the atoms of a σ-algebra coincide with the atoms of a measure. The study also investigates ℱ-atoms in trace σ-algebra and pre-image σ-algebra. The concept of quarks is introduced as a generalization of ℱ-atoms which is then used in characterizing atoms in product σ-algebra.