کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4623499 | 1339517 | 2007 | 8 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Mapping properties that preserve convergence in measure on finite measure spaces
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
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چکیده انگلیسی
Given a finite measure space (X,M,μ) and given metric spaces Y and Z, we prove that if is a sequence of arbitrary mappings that converges in outer measure to an M-measurable mapping and if is a mapping that is continuous at each point of the image of f, then the sequence g○fn converges in outer measure to g○f. We must use convergence in outer measure, as opposed to (pure) convergence in measure, because of certain set-theoretic difficulties that arise when one deals with nonseparably valued measurable mappings. We review the nature of these difficulties in order to give appropriate motivation for the stated result.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 326, Issue 2, 15 February 2007, Pages 1116-1123
Journal: Journal of Mathematical Analysis and Applications - Volume 326, Issue 2, 15 February 2007, Pages 1116-1123