  The notion of expansivity and its generalizations (measure expansive, measure
positively expansive, continuum-wise expansive, countably-expansive) are well
known for deterministic systems and can be a useful property for significant
behavior such as chaotic one. This study aims to extend these notions into a
random context and prove a relationship between relative positive entropy and
random expansive measure and apply it to show that if a random dynamical system
has positive relative topological entropy so the $w$-stable classes have zero
measure for the conditional measures. We also prove that there exists a
probability measure that is both invariant and expansive. Moreover, we obtain a
relation between the notions of random expansive measure and random
countably-expansive.
