Resumen de Linear recurrence relations on measurable sets

Hajrudin Fejzic, G. Freiling, D. Rinne

• 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}.