Extension theorems of Tietze and Hahn-Banach play an important part in functional analysis. It seems reasonable to deal with similar questions for random transforms. In the present paper some measurability problems arising in connection with this probabilistic generalization are solved.
"Measurability of Extensions of Continuous Random Transforms." Ann. Math. Statist. 30 (4) 1152 - 1157, December, 1959. https://doi.org/10.1214/aoms/1177706100