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Multiple integration on time scales. (English) Zbl 1095.26006

This article deals with Darboux/Riemann integration theory on products of (two) time scales, a times scale being a closed subset or the reals. The foundation of the theory follows the classical theory. After defining the basic notion of an integral and proving results surrounding mean value properties a theory of Jordan-\(\Delta\)-measurable sets is established. Necessary generalizations are mainly technical. Coordinate transformations are not considered.

MSC:

26B15 Integration of real functions of several variables: length, area, volume
39A10 Additive difference equations
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