Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774440 | Journal of Mathematical Analysis and Applications | 2017 | 20 Pages |
Abstract
We introduce a pseudometric TV on the set MX of all functions mapping a rectangle X on the plane R2 into a metric space M, called the total joint variation. We prove that if two sequences {fj} and {gj} of functions from MX are such that {fj} is pointwise precompact on X, {gj} is pointwise convergent on X with the limit gâMX, and the limit superior of TV(fj,gj) as jââ is finite, then a subsequence of {fj} converges pointwise on X to a function fâMX such that TV(f,g) is finite. One more pointwise selection theorem is given in terms of total ε-variations (ε>0), which are approximations of the total variation as εâ0.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Vyacheslav V. Chistyakov, Svetlana A. Chistyakova,