Geodesic
An example of a~zero series expansion in the Walsh system
Matematičeskie zametki, Tome 19 (1976) no. 2, pp. 179-186.

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We construct an example of a zero series expansion in the Walsh system which converges to zero outside some closed $M$ set of zero measure and converges to $+\infty$ at each point of this set. This shows, in particular, that in the theorem which says that a Walsh series which converges everywhere to a finite symmetric function is a Fourier series it is impossible to omit the requirement of finiteness and allow convergence of the series on a set of zero measure to an infinity of specified sign. 
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     author = {V. A. Skvortsov},
     title = {An example of a~zero series expansion in the {Walsh} system},
     journal = {Matemati\v{c}eskie zametki},
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     number = {2},
     year = {1976},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_2_a2/}
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V. A. Skvortsov. An example of a~zero series expansion in the Walsh system. Matematičeskie zametki, Tome 19 (1976) no. 2, pp. 179-186. http://geodesic.mathdoc.fr/item/MZM_1976_19_2_a2/