Missouri Journal of Mathematical Sciences

Direct Proofs of the Fundamental Theorem of Calculus for the Omega Integral

C. Bryan Dawson and Matthew Dawson

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When introduced in a 2018 article in the American Mathematical Monthly, the omega integral was shown to be an extension of the Riemann integral. Although results for continuous functions such as the Fundamental Theorem of Calculus follow immediately, a much more satisfying approach would be to provide direct proofs not relying on the Riemann integral. This note provides those proofs.

Article information

Missouri J. Math. Sci., Volume 31, Issue 1 (2019), 46-55.

First available in Project Euclid: 30 May 2019

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Mathematical Reviews number (MathSciNet)

Primary: 26E35: Nonstandard analysis [See also 03H05, 28E05, 54J05]

omega integral fundamental theorem of calculus


Dawson, C. Bryan; Dawson, Matthew. Direct Proofs of the Fundamental Theorem of Calculus for the Omega Integral. Missouri J. Math. Sci. 31 (2019), no. 1, 46--55. doi:10.35834/mjms/1559181625. https://projecteuclid.org/euclid.mjms/1559181625

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