An elementary way to introduce a Perron-like integral

Details An elementary way to introduce a Perron-like integral An elementary way to introduce a Perron-like integral

2010-02-15

arxiv.org/abs/1002.2852v1

Ann. Acad. Sci. Fenn. Math. 36 (2011), no. 1, 153-164

Mathematics

Classical Analysis and ODEs

Scientific paper

10.5186/aasfm.2011.3609

We give an alternative definition of integral at the generality of the Perron integral and propose an exposition of the foundations of integral theory starting from this new definition. Both definition and proofs needed for the development are unexpectedly simple. We show how to adapt the definition to cover the multidimensional and Stieltjes case and prove that our integral is equivalent to the Henstock-Kurzweil(-Stieltjes) integral.

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