the dominated convergence theorem to derive Grönwall's inequality. References See also Stochastic Gronwall inequality Logarithmic norm, for a version of Gronwall's lemma that gives upper and lower bounds to the norm of the state transition matrix. Halanay inequality. A similar inequality to Gronwall's lemma that is used for differential equations with delay. Lemmas in analysis Ordinary differential equations Stochastic differential equations Articles containing proofs Probabilistic inequalities