Random product of quasi-periodic cocycles

Given a finite set of quasi-periodic cocycles the random product them is defined as composition according to some probability measure. We prove that $C^r$, $0\leq r \leq \infty$ (or analytic) $k+1$-tuples quasi periodic taking values in $SL_2(\mathbb{R})$ such has positive Lyapunov exponent contains $C^0$ open and $C^r$ dense subset which formed by continuity point For $GL_d(\mathbb{R})$ for $d>2$, we if one diagonal, then there exists simples spectrum are exponent.