Geodesic
On a generalization of Henstock-Kurzweil integrals
Mathematica Bohemica, Tome 144 (2019) no. 4, pp. 393-422.

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We study a scale of integrals on the real line motivated by the $MC_{\alpha }$ integral by Ball and Preiss and some recent multidimensional constructions of integral. These integrals are non-absolutely convergent and contain the Henstock-Kurzweil integral. Most of the results are of comparison nature. Further, we show that our indefinite integrals are a.e. approximately differentiable. An example of approximate discontinuity of an indefinite integral is also presented.
DOI : 10.21136/MB.2019.0038-19
Classification : 26A39
Keywords: Henstock-Kurzweil integral 
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Malý, Jan; Kuncová, Kristýna. On a generalization of Henstock-Kurzweil integrals. Mathematica Bohemica, Tome 144 (2019) no. 4, pp. 393-422. doi : 10.21136/MB.2019.0038-19. http://geodesic.mathdoc.fr/articles/10.21136/MB.2019.0038-19/

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