The support of a real-valued function f on a topological space is the closure of {x : f (x ) /= 0}. Let L be the set of continuous real-valued functions on R with compact support.
(a) Show that ( f dµ is defined for any f ∈ L and Radon measure µ.
(b) Show that L is a Stone vector lattice as defined in §4.5.
(c) Show that if I is linear from L into R and I ( f ) ≥ 0 whenever f ≥ 0, then L is a pre-integral.