A NOTE ON THE HAUSDORFF DIMENSION OF SOME LIMINF SETS APPEARING IN SIMULTANEOUS DIOPHANTINE APPROXIMATION
A NOTE ON THE HAUSDORFF DIMENSION OF SOME LIMINF SETS APPEARING IN SIMULTANEOUS DIOPHANTINE APPROXIMATION
Let Q be an infinite set of positive integers. Denote by W_{\tau, n}(Q) (resp. W_{\tau, n}) the set of points in dimension n simultaneously \tau--approximable by infinitely many rationals with denominators in Q (resp. in N*). A non--trivial lower bound for the Hausdorff dimension of the liminf set W_{\tau, n}\W_{\tau, …