Geodesic
Another Perron type integration in $n$ dimensions as an extension of integration of stepfunctions
Czechoslovak Mathematical Journal, Tome 47 (1997) no. 3, pp. 557-575.

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For a new Perron-type integral a concept of convergence is introduced such that the limit $f$ of a sequence of integrable functions $f_k$, $ k \in \mathbb N$ is integrable and any integrable $f$ is the limit of a sequence of stepfunctions $g_k$, $ k \in \mathbb N$.
Classification : 26A39, 26B99 
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     author = {Jarn{\'\i}k, Ji\v{r}{\'\i} and Kurzweil, Jaroslav},
     title = {Another {Perron} type integration in $n$ dimensions as an extension of integration of stepfunctions},
     journal = {Czechoslovak Mathematical Journal},
     pages = {557--575},
     publisher = {mathdoc},
     volume = {47},
     number = {3},
     year = {1997},
     mrnumber = {1461432},
     zbl = {0902.26006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_1997__47_3_a13/}
}
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Jarník, Jiří; Kurzweil, Jaroslav. Another Perron type integration in $n$ dimensions as an extension of integration of stepfunctions. Czechoslovak Mathematical Journal, Tome 47 (1997) no. 3, pp. 557-575. http://geodesic.mathdoc.fr/item/CMJ_1997__47_3_a13/