2019/03/13 by Abraham Westerbaan, Westerbaan, Abraham A.
Computer Science · #Data Management and Algorithms #FOS: Mathematics #Functional Analysis (math.FA) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.1903.06044
openalex publication_date 2019/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Measure and integral are two closely related, but distinct objects of study. Nonetheless, they are both real-valued lattice valuations: order preserving real-valued functions ϕ on a lattice L which are modular, i.e., ϕ(x)+ϕ(y) = ϕ(x\wedge y)+ϕ(x\vee y) for all x,y ∈ L. We unify measure and integral by developing a theory for lattice valuations. We allow these lattice valuations to take their values from the reals, or any suitable ordered Abelian group.