کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6418860 | 1339362 | 2013 | 12 صفحه PDF | دانلود رایگان |
Given a rectangle in the real Euclidean n-dimensional space and two maps f and g defined on it and taking values in a metric semigroup, we introduce the notion of the total joint variation TV(f,g) of these maps. This extends similar notions considered by Hildebrandt (1963) [17], Leonov (1998) [18], Chistyakov (2003, 2005) [5,8] and the authors (2010). We prove the following irregular pointwise selection principle in terms of the total joint variation: if a sequence of maps {fj}j=1â from the rectangle into a metric semigroup is pointwise precompact and lim supj,kââ TV(fj,fk) is finite, then it admits a pointwise convergent subsequence (whose limit may be a highly irregular, e.g., everywhere discontinuous, map). This result generalizes some recent pointwise selection principles for real functions and maps of several real variables.
Journal: Journal of Mathematical Analysis and Applications - Volume 402, Issue 2, 15 June 2013, Pages 648-659