The structure on invariant measures of C1 generic diffeomorphisms

Let I > be an isolated non-trivial transitive set of a C (1) generic diffeomorphism f a Diff(M). We show that the space of invariant measures supported on I > coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in I > (which implies that the set of irregular(+) points is also residual in I >). As an application, we show that the non-uniform hyperbolicity of irregular(+) points in I > with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in I >) determines the uniform hyperbolicity of I >.