Geodesic
On the local behaviour of the multidimensional $\Lambda$-variation
Sbornik. Mathematics, Tome 201 (2010) no. 11, pp. 1563-1578

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Let two classes $(\Lambda^1,\dots,\Lambda^m)BV$ and $(M^1,\dots,M^m)BV$ on an interval $\Delta$ be given. In the paper, we find necessary and sufficient conditions for the $\Lambda$-variation of any function in the $M$-class, over a neighbourhood of every regular point, to tend to zero as the neighbourhood decreases. Bibliography: 10 titles.
Keywords: generalized variation, regular point, variation over a neighbourhood. 
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     author = {A. N. Bakhvalov},
     title = {On the local behaviour of the multidimensional $\Lambda$-variation},
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     number = {11},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2010_201_11_a0/}
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A. N. Bakhvalov. On the local behaviour of the multidimensional $\Lambda$-variation. Sbornik. Mathematics, Tome 201 (2010) no. 11, pp. 1563-1578. http://geodesic.mathdoc.fr/item/SM_2010_201_11_a0/