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

2018/03/20 by C. Bryan Dawson, Matthew Dawson, Dawson, C. Bryan +1
Mathematics · #26E35 #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical and Theoretical Analysis #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1803.09633

openalex publication_date 2018/03/20 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

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

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