Geodesic
Some generalizations of uniqueness theorems for series in Walsh~systems
Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 367-372

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We determine conditions on the behavior of the partial sums of a Walsh series outside a certain $U$-set, under which this series is a Fourier–Walsh series. 
@article{MZM_1973_13_3_a4,
     author = {V. A. Skvortsov},
     title = {Some generalizations of uniqueness theorems for series in {Walsh~systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {367--372},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a4/}
}
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V. A. Skvortsov. Some generalizations of uniqueness theorems for series in Walsh~systems. Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 367-372. http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a4/