A Lifting Theorem for Locally Convex Subspaces of Lo

Abstract

We prove that for every closed locally convex subspace $E$ of $L_0$ and for any continuous linear operator $T$ from $L_0$ to $L_0/E$ there is a continuous linear operator $S$ from $L_0$ to $L_0$ such that $T=QS$ where $Q$ is the quotient map from $L_0$ to $L_0/E$.