Let be a measure space and let denote the set of positive measurable functions endowed with the topology of convergence in measure with respect to Then by Fatou's lemma the integral, seen as an operator from to is lower semicontinuous.
Let be a measure space and let denote the set of positive measurable functions endowed with the topology of convergence in measure with respect to Then by Fatou's lemma the integral seen as an operator from to is lower semicontinuous