Geodesic
Decomposition of dyadic measures and unions of closed $\mathscr{U}$-sets for series in a~Haar system
Sbornik. Mathematics, Tome 207 (2016) no. 3, pp. 444-457

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New properties of finitely additive set functions (quasi-measures) and Borel measures on dyadic product groups $\mathbb{G}^m$ are established. The results obtained are applied to the theory of series in Haar systems — for example, for a broad family of classes of multiple Haar series on $\mathbb{G}^m$, a countable union of closed uniqueness sets is shown to be a uniqueness set too. Bibliography: 18 titles.
Keywords: multiple Haar series, quasi-measure, Borel measure.
Mots-clés : dyadic product group, $\mathscr{U}$-set 
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     author = {M. G. Plotnikov and Yu. A. Plotnikova},
     title = {Decomposition of dyadic measures and unions of closed $\mathscr{U}$-sets for series in {a~Haar} system},
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M. G. Plotnikov; Yu. A. Plotnikova. Decomposition of dyadic measures and unions of closed $\mathscr{U}$-sets for series in a~Haar system. Sbornik. Mathematics, Tome 207 (2016) no. 3, pp. 444-457. http://geodesic.mathdoc.fr/item/SM_2016_207_3_a6/