Displaying similar documents to “Definition of the definite integral”

A descriptive, additive modification of Mawhin's integral and the Divergence Theorem with singularities

Dirk Jens F. Nonnenmacher (1994)

Annales Polonici Mathematici

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Modifying Mawhin's definition of the GP-integral we define a well-behaved integral over n-dimensional compact intervals. While its starting definition is of Riemann type, we also establish an equivalent descriptive definition involving characteristic null conditions. This characterization is then used to obtain a quite general form of the divergence theorem.

A concept of absolute continuity and a Riemann type integral

B. Bongiorno, Washek Frank Pfeffer (1992)

Commentationes Mathematicae Universitatis Carolinae

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We present a descriptive definition of a multidimensional generalized Riemann integral based on a concept of generalized absolute continuity for additive functions of sets of bounded variation.