An Extension of the 1-Dim Lebesgue Integral of a Product of Two Functions

Clara Carlota () and António Ornelas
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Clara Carlota: Departamento de Matemática, CIMA, Universidade de Évora, 7000-671 Évora, Portugal
António Ornelas: Departamento de Matemática, CIMA, Universidade de Évora, 7000-671 Évora, Portugal

Mathematics, 2023, vol. 11, issue 15, 1-16

Abstract: In this paper, our main aim is to present a reasonable extension of the 1-dim Lebesgue integral of the product of two functions, in case this Lebesgue integral does not exist (i.e., the integrals of its negative and positive parts are both ∞ ). This extension works fine quite generally, as shown by several examples, and it is based on general hypotheses guaranteeing the sign of the integral (in the sense of being necessarily <0 or =0 or else >0), without computing its actual value. For this purpose, our method provides much more precise results than the Lebesgue–Stieltjes integration by parts.

Keywords: extension of the 1-dim Lebesgue integral of a product; integral inequalities; Lebesgue–Stieltjes integration by parts (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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