کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4673148 | 1346612 | 2013 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
New results on integration on the Levi-Civita field
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: New results on integration on the Levi-Civita field New results on integration on the Levi-Civita field](/preview/png/4673148.png)
چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Indagationes Mathematicae - Volume 24, Issue 1, 2013, Pages 199-211
Journal: Indagationes Mathematicae - Volume 24, Issue 1, 2013, Pages 199-211
نویسندگان
Khodr Shamseddine,