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On the existence of the Stieltjes integral

1925
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Transactions of the American Mathematical Society
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Lebesguet has shown how to treat the Riemann integral by studying the content of an associated point set. The present paper is an attempt in the same direction for the Stieltjes integral. A pair of conditions are found which are necessary and sufficient for the existence of the integral, one of which concerns itself with the associated point set. The other is automatically satisfied for a large class of integrals comprising (1) those for which the associated point set is a (continuous) curve

doi:10.1090/s0002-9947-1925-1501324-5
fatcat:vvd4sok445hgvffvt3w25sfhwa