Geodesic
On the total variation for functions of several variables and a multidimensional analog of Helly's selection principle
Matematičeskie zametki, Tome 63 (1998) no. 1, pp. 69-80.

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We introduce the new notion of total variation for the Hardy class of functions of several variables and state various properties, similar to those in the one-dimensional case, for functions belonging to this class. In particular, we prove a precise version of Helly's selection principle for this class. 
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A. S. Leonov. On the total variation for functions of several variables and a multidimensional analog of Helly's selection principle. Matematičeskie zametki, Tome 63 (1998) no. 1, pp. 69-80. http://geodesic.mathdoc.fr/item/MZM_1998_63_1_a7/

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