Let A(x,n) be the cocycle over f, where f is an measure preserving transformation on a probability space X. Is the largest Lyapunov exponent always given by

\lim_{n\to +\infty} \log ||A(x,n)||?

Since the above limit can be bounded from above by \int_X\log ||A|| can one give an example of the cocycle where the above inequality is strict? Tnx!