Linear recurrence relations on measurable sets
- Autores: Hajrudin Fejzic, G. Freiling, D. Rinne
- Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 82, Nº 3, 2010, págs. 717-732
- Idioma: inglés
- DOI: 10.1112/jlms/jdq055
- Enlaces
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Resumen
Let A1, . . . , Am be measurable sets, whose characteristic functions are denoted by A1(x), . . . , Am(x). Let c1, . . . , cm be any real numbers and for each i = 1, . . . , m let {ai,k}�� k=1 be a sequence of real numbers converging to zero. Suppose m i=1 ciAi(x + ai,k) = 0 for each k = 1, 2, . . . and for almost every x. Then, for all sufficiently large k and all y, ciAi(x)�Ôy(ai,k) is constant almost everywhere, where �Ôy is the characteristic function of {y}.
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