On Non-Absolute Integrals

Varayu Boonpogkrong

Abstract




The Riemann integral, McShane integral and Henstock integral are well-known. They are the Riemann approach integrals. In this note we introduce the Riemann $\mathcal B$-integral using Riemann approach, which are non-absolute integrals. The Fundamental Theorem of Calculus is proved. The ``local Character" plays very important role in the prove of the Fundamental Theorem of Calculus. Some convergence theorems are also proved.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|