Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4673148 | Indagationes Mathematicae | 2013 | 13 Pages |
Abstract
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)Â [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 over A are equal. We also show that if AâR is measurable and if (fn) is a sequence of measurable functions that converge uniformly on A to f, then f itself is measurable on A and its integral over A is given by â«Af=limnâââ«Afn.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Khodr Shamseddine,