Geodesic
Perron Integrability Versus Lebesgue Integrability
Canadian mathematical bulletin, Tome 28 (1985) no. 4, pp. 463-468

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The paper investigates the relationship between Perron - Stieltjes integrability and Lebesgue-Stieltjes integrability within the generalized Riemann approach. The main result states that with certain restrictions a Perron-Stieltjes integrable function is locally Lebesgue-Stieltjes integrable on an open dense set. This is then applied to show that a nonnegative Perron-Stieltjes integrable function is Lebesgue-Stieltjes integrable. Finally, measure theory is invoked to remove the restrictions in the main result.
DOI : 10.4153/CMB-1985-055-1
Mots-clés : 26A39, 26A42 
Schurle, Arlo W. Perron Integrability Versus Lebesgue Integrability. Canadian mathematical bulletin, Tome 28 (1985) no. 4, pp. 463-468. doi: 10.4153/CMB-1985-055-1
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     author = {Schurle, Arlo W.},
     title = {Perron {Integrability} {Versus} {Lebesgue} {Integrability}},
     journal = {Canadian mathematical bulletin},
     pages = {463--468},
     year = {1985},
     volume = {28},
     number = {4},
     doi = {10.4153/CMB-1985-055-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-055-1/}
}
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