Spaces of measurable functions on the Levi-Civita field
نویسندگان
چکیده
منابع مشابه
On the topological structure of the Levi-Civita field
Article history: Received 22 June 2009 Available online 19 February 2010 Submitted by B. Sims
متن کاملMeasure Theory and Integration on the Levi-civita Field
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...
متن کاملAnalysis on the Levi - Civita field , a brief overview
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...
متن کاملAnalysis on the Levi-Civita field and computational applications
Keywords: Non-Archimedean analysis Levi-Civita fields Power series Measure theory and integration Optimization Computational applications This paper is dedicated to the loving memory of my brother Saïd Shamseddine (1968–2013). a b s t r a c t In this paper, we present an overview of some of our research on the Levi-Civita fields R and C. R (resp. C) is the smallest non-Archimedean field extensi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2020
ISSN: 0019-3577
DOI: 10.1016/j.indag.2020.06.005