This talk is online only on zoom meeting ID: 986 2892 7517

In the study of measure theory, we develop Lebesgue integration to extend the class of functions that can be integrated, beyond Riemann integrable functions. The typical path of this development is not particularly straightforward, as it requires us to first introduce the concepts of sigma algebras and measures.

In this talk I describe an alternative approach to Lebesgue integration originally developed by Professor Peter Lax. We start by defining the space of Lebesgue integrable functions on a rectangular box as the completion of the space of continuous functions on this box under the \(L^1\)-norm. Following this, the measurable subsets of this rectangular box are exactly those sets whose characteristic function is Lebesgue integrable. This approach is more amenable to the study of function analysis, contrasting the standard method which is better suited for the study of probability theory.