Geodesic
Perfect Sets of Uniqueness on the Group 2ω
Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 759-764

Voir la notice de l'article provenant de la source Cambridge University Press

Let ω 0, ω 1, ... denote the Walsh-Paley functions and let G denote the dyadic group introduced by Fine [3]. Recall that a subset E of G is said to be a set of uniqueness if the zero series is the only Walsh series ∑ akωk which satisfies A subset E of G which is not a set of uniqueness is called a set of multiplicity.It is known that any subset of G of positive Haar measure is a set of multiplicity [5] and that any countable subset of G is a set of uniqueness [2]. As far as uncountable subsets of Haar measure zero are concerned, both possibilities present themselves. Indeed, among perfect subsets of G of Haar measure zero there are sets of multiplicity [1] and there are sets of uniqueness [5]. 
Yoneda, Kaoru. Perfect Sets of Uniqueness on the Group 2ω. Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 759-764. doi: 10.4153/CJM-1982-052-1
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