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Relationship between the Riemann and Lebesgue Integrals

   | 09. Juli 2022

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The goal of this article is to clarify the relationship between Riemann and Lebesgue integrals. In previous article [5], we constructed a one-dimensional Lebesgue measure. The one-dimensional Lebesgue measure provides a measure of any intervals, which can be used to prove the well-known relationship [6] between the Riemann and Lebesgue integrals [1]. We also proved the relationship between the integral of a given measure and that of its complete measure. As the result of this work, the Lebesgue integral of a bounded real valued function in the Mizar system [2], [3] can be calculated by the Riemann integral.

eISSN:
1898-9934
Sprache:
Englisch
Zeitrahmen der Veröffentlichung:
Volume Open
Fachgebiete der Zeitschrift:
Informatik, andere, Mathematik, Allgemeines