Tonelli

Tonelli is an Italian surname. In mathematics, it is associated with two notable concepts: Tonelli's theorem and the Tonelli–Shanks algorithm. Tonelli's theorem, named after the Italian mathematician Tonelli, is a result in measure theory that allows the interchange of the order of integration for nonnegative measurable functions on a product measure space, stating that the double integral equals the iterated integrals. The Tonelli–Shanks algorithm, named jointly for Tonelli and Daniel Shanks, provides an efficient method for computing modular square roots modulo an odd prime p, solving x^2 ≡ a (mod p). The Tonelli surname has been carried by several Italian scholars and scientists, particularly in mathematics. As with many Italian surnames, it reflects regional origins.