#### Document Type

Article - postprint

#### Department

Mathematics (CMC)

#### Publication Date

4-2004

#### Abstract

In a recent paper [1] the two authors of this note have shown that Fubini's theorem on changing the order of integration and Schwarz's lemma on the equality of mixed partial deriatives are equivalent when standard assumptions of continuity and differentiability are made. The proof relies heavily upon the fundamental theorem of integral calculus as usually presented in calculus textbooks. Fubini's theorem is regarded as intuitive and easy to prove. Therefore, the equivalence established in [1] with a straightforward argument provides a simple proof of Schwarz's lemma.

#### Rights Information

© 2004 MAA

#### Terms of Use & License Information

#### DOI

10.2307/4145243

#### Recommended Citation

Aksoy, A. Martelli, M., “Wave Equation, Mixed Partial Derivatives and Fubini’s Theorem” the American Mathematical Monthly, Vol. 111, 2004, N.4, 2004. doi: 10.2307/4145243