Triangle integral – a nonabsolute integration process suitable for piecewise linear surfaces. (English) Zbl 1243.26004

Kaufmann, Pedro L.; Bianconi, Ricardo

Real Anal. Exch. 36(2010-2011), No. 2, 373-404 (2011).

Using triangle-based partitions, in this paper the authors presented a two-dimensional nonabsolute gauge integral which satisfies several convergence theorems and a general divergence theorem, and at the same time admits a change of variables formula valid up to affine transformations – thus applicable to piecewise linear surfaces.

Reviewer: Jitan Lu (Singapore)

MSC:

26A39

Denjoy and Perron integrals, other special integrals

Keywords:

nonabsolute integration; triangle integral; convergence theorems; divergence theorem