  We prove that the Lyapunov exponents of random products in a (real or
complex) matrix group depends continuously on the matrix coefficients and
probability weights. More generally, the Lyapunov exponents of the random
product defined by any compactly supported probability distribution on $GL(d)$
vary continuously with the distribution, in a natural topology corresponding to
weak$^*$-closeness of the distributions and Hausdorff-closeness of their
supports.
