The unstable-manifold conditional-measure conjecture

Recall that a strongly simple action has one-dimensional coarse Lyapunov distributions, which integrate to Lyapunov foliations, and that some Lyapunov foliations have conditional measures equivalent to Lebesgue measure. Unstable-manifold conditional-measure conjecture. Conditional measures on unstable manifolds of action elements should be equivalent to Lebesgue measures on certain smooth submanifolds obtained by integrating those Lyapunov foliations for which the conditional measures are Lebesgue. This is presented as a possible strengthening of the preceding theorem; the source does not give a resolution.