Arithmetic of (independent) sigma-fields on probability spaces

Abstract

This note gathers what is known about, and provides some new results concerning the operations of intersection, of “generated σ-field”, and of “complementation” for (independent) complete σ-fields on probability spaces.

Keywords

• Lattice of complete <italic>σ</italic>-fields
• generated <italic>σ</italic>-field
• intersection of <italic>σ</italic>-fields
• independent complements