Leonida Tonelli was born on 19 April, 1885 in the city of Gallipoli in the southern region Apulia of Italy. He was educated at the University of Bologna, receiving a doctoral degree in 1907. Tonelli held faculty positions in several universities in Italy, including the University of Cagliari, the University of Parma, the University of Bolgna, and the University of Pisa. He also served in World War I. Tonelli died on 12 March 1946 in Pisa, Italy.
Tonelli's mathematical contributions are mainly in analysis, including the calculus of variations, Fourier series (named for Joseph Fourier), and Lebesgue integration (named for Henri Lebesgue). He is best known for the theorem, now named for him, that states that the double integral of a nonnegative function over a product measure space is the same as the corresponding iterated integrals. Tonelli's theorem is often thought of as a special case of Fubnini's theorem, named for Guido Fubini. Both theorems are important in probability as in many other branches of analysis.