Deficient topological measures on locally compact spaces

Topological measures and quasi-linear functionals generalize linear functionals. We define study deficient topological on locally compact spaces. A measure a space is set function open closed sets which finitely additive sets, inner regular outer sets. Deficient measures. First we investigate positive, negative, total variation of signed that only assumed to be These variations turn out Then examine finite additivity, superadditivity, smoothness, other properties obtain methods for generating new provide necessary sufficient conditions measure. The results presented are further measures, corresponding non-linear