This process is named for a mathematician who also names the measure on which it is based.
Daniell names an axiomatized alternative to this process. Fatou's lemma relates this operation on the limit inferior of a sequence of functions to the limit inferior of the sequence of this operation of those functions. A theorem states that if a sequence of functions fn is all less than a function g on which this process can be performed, then this process can be performed on the limit of that sequence; that is the   dominated convergence theorem. This process is named for a mathematician who also names the measure on which it is based. For ten points, identify this more powerful generalization of the Riemann integral.
Daniell names an axiomatized alternative to this process. Fatou's lemma relates this operation on the limit inferior of a sequence of functions to the limit inferior of the sequence of this operation of those functions.
Lebesgue integral [accept word forms, prompt on integral and word forms, do not accept or prompt on any other sort of integral like  Darboux integral  ]