An Incompatibility Result on non-Archimedean Integration

We prove that a Riemann-like integral on non-Archimedean extensions of 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 inco...

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Veröffentlicht in:	P-adic numbers, ultrametric analysis, and applications ultrametric analysis, and applications, 2021-10, Vol.13 (4), p.316-319
1. Verfasser:	Bottazzi, Emanuele
Format:	Artikel
Sprache:	eng
Schlagworte:	14/34 639/766/189 639/766/530 639/766/747 Algebra Incompatibility Mathematics Mathematics and Statistics
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Zusammenfassung:	We prove that a Riemann-like integral on non-Archimedean extensions of 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.
ISSN:	2070-0466 2070-0474
DOI:	10.1134/S2070046621040063