  It is known that nonuniformly hyperbolic maps admitting singularities have at
most countably many ergodic Sinai-Ruelle-Bowen (SRB) measures. These maps
include the Belykh attractor, the geometric Lorenz attractor, and more general
Lorenz-type systems. In this paper, we establish easily verifiable sufficient
conditions guaranteeing that the number of ergodic SRB measures is at most
finite, and provide examples and nonexamples showing that the conditions are
necessary in general.
