Quasi-linear functionals on locally compact spaces

This paper combines new and known results in a single convenient source for anyone interested learning about quasi-linear functionals on locally compact spaces. We define singly generated subalgebras different settings study signed positive functionals. Quasi-linear are, general, nonlinear, but linear subalgebras. The gives representation theorems C c (X), bounded 0 (X) space, C(X) space. There is an order-preserving bijection between compact-finite topological measures, which also “isometric” when measures are finite. present many properties of give explicit example functional ℝ 2 . Results the will be helpful further application areas mathematics, including symplectic geometry.