The Fubini Theorem

Abstract

The Fubini theorem belongs to the most powerful tools in Analysis. It is very useful in practical calculations and, besides, plays a striking role in proving several important theorems on integration. The Fubini theorem establishes a connection between the so called double integrals and repeated integrals. The proofs given in text books are usually difficult. Using our definitions of the Lebesgue or the Bochner integrals, the proof becomes surprisingly simple and reduces in fact to various interpretations of the same definition.