  Let (M,d) be a compact metric space and f:M --> M an expansive homeomorphism.
We define Lyapunov exponents L(f,m)_{max} and l(f,mu)_{min} for an f-invariant
measure m. When L(f,m)_{max} > 0 and l(f,mu)_{min} < 0 can be interpreted as a
weak form of hyperbolicity for f. We prove that if M is a Peano space then
there is g>0 such that L(f,m)_{max} > g and l(f,m)_{min}< - g. We also show
that the hypothesis that M is a Peano space is necessary to obtain the maximal
Lyapunov exponent positive and the minimal Lyapunov exponent negative. Moreover
we define Lyapunov exponents for K, a compact f-invariant subset of M and prove
that if the maximal Lyapunov exponent of K is negative then K is an attractor.
When f is a diffeomorphism on a compact manifold, these Lyapunov exponents
coincide with the usual ones.
