Intermediate Value Theorem for Analytic Functions on a Levi-Civita Field
نویسندگان
چکیده
منابع مشابه
Intermediate Value Theorem for Analytic Functions on a Levi-Civita Field
The proof of the intermediate value theorem for power series on a LeviCivita field will be presented. After reviewing convergence criteria for power series [19], we review their analytical properties [18]. Then we state and prove the intermediate value theorem for a large class of functions that are given locally by power series and contain all the continuations of real power series: using iter...
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The proofs of the extreme value theorem, the mean value theorem and the inverse function theorem for analytic functions on the Levi-Civita field will be presented. After reviewing convergence criteria for power series [15], we review their analytical properties [18, 20]. Then we derive necessary and sufficient conditions for the existence of relative extrema for analytic functions and use that ...
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In this paper, we review the algebraic properties of various nonArchimedean ordered structures, extending them in various steps which lead naturally to the smallest non-Archimedean ordered field that is Cauchy-complete and real closed. In fact, the Levi-Civita field is small enough to allow for the calculus on the field to be implemented on a computer and used in applications such as the fast a...
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It is well known that the disconnectedness of a non-Archimedean totally ordered field in the order topology makes integration more difficult than in the real case. In this paper, we present a remedy to that difficulty and study measure theory and integration on the Levi-Civita field. After reviewing basic elements of calculus on the field, we introduce a measure that proves to be a natural gene...
متن کاملNew results on integration on the Levi-Civita field
New results for integration of functions on the Levi-Civita field R are presented in this paper which is a continuation of the work done in Shamseddine and Berz (2003) [13] and complements it. For example, we show that if f and g are bounded on a measurable set A and f = g almost everywhere on A then f is measurable on A if and only if g is measurable on A in which case the integrals of f and g...
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2007
ISSN: 1370-1444
DOI: 10.36045/bbms/1197908910