Abstract
We prove that a Riemann-like integral on non-Archimedean extensions of \(\mathbb{R}\) cannot assign an integral to every function whose standard part is measurable and simultaneously satisfy the fundamental theorem of calculus. We also discuss how existing theories of non-Archimedean integration deal with the incompatibility of these conditions.
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Bottazzi, E. An Incompatibility Result on non-Archimedean Integration. P-Adic Num Ultrametr Anal Appl 13, 316–319 (2021). https://doi.org/10.1134/S2070046621040063
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DOI: https://doi.org/10.1134/S2070046621040063