  For any continuous map f on a compact manifold M, we define the SRB-like (or
observable) probabilities as a generalization of Sinai-Ruelle-Bowen (i.e.
physical) measures. We prove that f has observable measures, even if SRB
measures do not exist. We prove that the definition of observability is
optimal, provided that the purpose of the researcher is to describe the
asymptotic statistics for Lebesgue almost every initial state. Precisely, the
never empty set O of all the observable measures, is the minimal weak*-compact
set of Borel probabilities in M that contains the limits (in the weak*
topology) of all the convergent subsequences of the empiric probabilities for
Lebesgue almost all x in M. We prove that any isolated measure in O is SRB.
Finally we conclude that if O is finite or countable infinite, then there exist
(up to countable many) SRB measures such that the union of their basins cover M
Lebesgue a.e.
