Lattice Valuations: a Generalisation of Measure and Integral

Abstract

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 $\varphi$ on a lattice $L$ which are modular, i.e., $\varphi (x)+\varphi (y)=\varphi (x\wedge y)+\varphi (x\vee y)$ for all $x,y\in L$. 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.

Master's thesis