On maxitive integration

Cattaneo, Marco E. G. V. (22. August 2013): On maxitive integration. Department of Statistics: Technical Reports, No.147

Abstract

The Shilkret integral is maxitive (i.e., the integral of a pointwise supremum of functions is the supremum of their integrals), but defined only for nonnegative functions. In the present paper, some properties of this integral (such as subadditivity and a law of iterated expectations) are studied, in comparison with the additive and Choquet integrals. Furthermore, the definition of a maxitive integral for all real functions is discussed. In particular, a convex, maxitive integral is introduced and some of its properties are derived.

• Item Type: Paper
• Faculties: Mathematics, Computer Science and Statistics > Statistics > Technical Reports
• Subjects: 500 Science > 510 Mathematics
• Language: English