Nonabsolutely convergent integrals via integral sums in $Rⁿ$

Year, pages: 1996, 191 - 201

The integral considered is defined as a limit of Riemannian integral sums by an unconspicuous change in the original limiting process. It is an extension of the Lebesgue integral and in the one-dimensional case it coincides with the integrals of Denjoy and of Perron. For this type of integral the following properties are discussed: relation of integrals and primitives, integration of derivatives, Stokes Theorem, transformations, convergence theorems, density of the set of step functions in the space of integrable functions.

Kurzweil, J. 1996. Nonabsolutely convergent integrals via integral sums in $Rⁿ$. In Tatra Mountains Mathematical Publications, vol. 8, no.2, pp. 191-201. 1210-3195.

Kurzweil, J. (1996). Nonabsolutely convergent integrals via integral sums in $Rⁿ$. Tatra Mountains Mathematical Publications, 8(2), 191-201. 1210-3195.