Grönwall's inequality

It is named for Thomas Hakon Grönwall (1877–1932). Grönwall is the Swedish spelling of his name, but he spelled his name as Gronwall in his scientific publications after emigrating to the United States.

Substituting this result into the assumed integral inequality gives Grönwall's inequality.

Using the Fubini–Tonelli theorem to interchange the two integrals, we obtain