On the integrals of Riemann-Lebesgue type
نویسندگان
چکیده
منابع مشابه
The Riemann and Lebesgue Integrals
§1 Preliminaries: Step Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 §2 Riemann Integrable Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 §3 Lebesgue measure zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 §4 Definition and Properties of the Lebesgue Integral . . . . . . . . . . 7 §5 The spaces L(R) and L(R) ....
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We show how two change-of-variables formulæ for Lebesgue–Stieltjes integrals generalize when all continuity hypotheses on the integrators are dropped. We find that a sort of “mass splitting phenomenon” arises. Let M : [a, b]→ R be increasing. Then the measure corresponding to M may be defined to be the unique Borel measure μ on [a, b] such that for each continuous function f : [a, b] → R, the i...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1997
ISSN: 0040-8735
DOI: 10.2748/tmj/1178225108