Strengthens the dominated-convergence theorem: the dominating hypothesis can be relaxed to uniform integrability. With convergence in measure and sup_n ∫_{|f_n|>M}|f_n| → 0 as M→∞, the sequence converges in the L¹ norm.
Strengthens the dominated-convergence theorem: the dominating hypothesis can be relaxed to uniform integrability. With convergence in measure and sup_n ∫_{|f_n|>M}|f_n| → 0 as M→∞, the sequence converges in the L¹ norm.