On the space of measurable functions and its topology determined by the Choquet integral

Let (X,A,μ)(X,A,μ) be a finite nonadditive measure space and MM be the set of all finite measurable functions on X  . The topology on MM, which is determined by the Choquet integral with respect to μ, is investigated. The relationship between this topology and the one determined by the Sugeno integral is examined. Some interesting examples are included.

► The topology of measurable function space determined by the Choquet integral is discussed.
► The relationship of our topology and that of Wu et al. is examined.
► Several interesting examples are included.