# \$E[X|mathcal{Q}] leq liminf_nE [X_n|mathcal{Q}]\$

If $$(X_n)_n$$ is a sequence of nonnegative random variable, $$mathcal{Q}$$ is a sub $$sigma$$-algebra, then almost surley $$E(liminf_n X_n|mathcal{Q}) leq liminf_n E(X_n|mathcal{Q}).$$

Let’s say that $$(X_n)_n$$ converges in probability to $$X,$$ is this true that, almost surely, $$E(X|mathcal{Q}) leq liminf_nE (X_n|mathcal{Q})$$