Pesin’s identity provides a profound connection between the Kolmogorov-Sinai entropy hKS and the Lyapunov exponent L. It is well known that many systems exhibit subexponential separation of nearby trajectories and then L=0. In many cases such systems are nonergodic and do not obey usual statistical mechanics. We investigate the nonergodic phase of the Pomeau-Manneville map where separation of nearby trajectories is stretched exponential. The limit distribution of L is the inverse Le´vy function. The average <L> is related to the infinite invariant density, and most importantly to entropy. Our work gives a generalized Pesin’s identity valid for systems with an infinite invariant density.