  We give explicit $C^1$-open conditions that ensure that a diffeomorphism
possesses a nonhyperbolic ergodic measure with positive entropy. Actually, our
criterion provides the existence of a partially hyperbolic compact set with
one-dimensional center and positive topological entropy on which the center
Lyapunov exponent vanishes uniformly.
  The conditions of the criterion are met on a $C^1$-dense and open subset of
the set of a diffeomorphisms having a robust cycle. As a corollary, there
exists a $C^1$-open and dense subset of the set of non-Anosov robustly
transitive diffeomorphisms consisting of systems with nonhyperbolic ergodic
measures with positive entropy.
  The criterion is based on a notion of a blender defined dynamically in terms
of strict invariance of a family of discs.
