Lebesgue's dominated convergence theorem.[1] Let ( f n ) {\displaystyle (f_{n})} be a sequence of complex-valued measurable functions on a measure space ( S , Σ , μ ) {\displaystyle (S,\Sigma ,\mu )} . Suppose that the sequence converges pointwise to a function f {\displaystyle f} and is dominated by some integrable function g {\displaystyle g} in the sense that