Conditional norm covariance under a factor map
= Conditional norm covariance under a factor map
{title2=$T_*\mu_y=\mu_{Sy},\quad\|U_T^nf\|_y=\|f\|_{S^ny}$}
For invertible probability systems linked by a <factor map>, invariance and uniqueness of disintegration identify the pushforward of each conditional measure with the conditional measure on the transformed fiber. The displayed norm identity follows for all integer times on a common full-measure set. It transports uniform conditional error bounds along whole orbits.