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Let p be a prime number. The p-adic case of the Mixed Littlewood Conjecturestates that liminf_{q \to \infty} q . |q|_p . ||q x|| = 0 for all real numbersx. We show that with the additional factor of log q.loglog q the statement isfalse. Indeed, our main result implies that the set of x for whichliminf_{q\to\infty} q . log q . loglog q. |q|_p . ||qx|| > 0 is of fulldimension. The result is obtained as an application of a general framework forCantor sets developed in this paper.

Multiplicatively badly approximable numbers and generalised Cantor sets