Topological and topological linear properties of the Sugeno-Lorentz spaces

Abstract

The properties of spaces of Sugeno integrable functions are quite different from those of ordinary spaces of Lebesgue integrable functions. In our previous research, given a nonadditive measure μ and constants 0<p<∞ and 0<q<∞, the completeness and separability of the Sugeno-Lorentz spaces were discussed with respect to the Sugeno-Lorentz prenorm (⋅)p,q. The purpose of the paper is to further advance our study of the Sugeno-Lorentz spaces from the perspective of topology. To this end, the Sugeno-Lorentz topologies are defined as the topologies generated by the prenorms (⋅)p,q. Some topological and topological linear properties of the Sugeno-Lorentz spaces are discussed. Of particular interest is that the Sugeno-Lorentz spaces and the Sugeno-Lorentz topologies are unique regardless of p and q.