The full-measure conjecture for conditions (I') and (II')

Let $\triangle$ be the simplex on which the TRIP map $T_G$ acts, and let conditions (I') and (II') be the conditions defined in the paper for the associated coding dynamics.

Full-measure conjecture. There is a subset of $\triangle$ of full Lebesgue measure on which condition (I') or condition (II') is satisfied.

The preceding proposition verifies these conditions on explicit sets and their iterated preimages. The conjecture asserts that the exceptional set contained in the invariant region $C$ has Lebesgue measure zero.