  In this paper we study the Mixed Littlewood Conjecture with pseudo-absolute
values. We show that if p is a prime and D is a pseudo-absolute value sequence
satisfying mild conditions then then the infimum over natural numbers n of the
quantity n.|n|_p.|n|_D.||nx|| equals 0 for all real x. Our proof relies on a
measure rigidity theorem due to Lindenstrauss and lower bounds for linear forms
in logarithms due to Baker and Wustholz. We also deduce the answer to the
related metric question of how fast the infimum above tends to zero, for almost
every x.
