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Quasi-linear functionals are shown to be uniformly continuous and decomposable into a difference of two quasi-integrals. A predual space for the quasi-linear functionals inducing the weak*-topology is given. General constructions of quasi-linear functionals by solid set-functions and q-functions are given. Proposition 15. Let X be a q-space. Let f be a q-function, and let ν be a normalized regular Borel (or topological) measure in X. Define µ on A s by: µC = f (νC); C ∈ C s and µU = f (1) −doi:10.1090/s0002-9947-06-03843-8 fatcat:oq73cfrfljgjjbfd6k47wnjhde