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