Gauge integral
Wednesday, June 22nd, 2005The gauge integral is a generalization of the Riemann and Lebesgue integrals. Interestingly, there are functions that can be integrated as improper Riemann integrals but are not Lebesgue integrable. The gauge integral also subsumes improper integrals. Lebesgue integrable functions turn out to be functions f such that both f and |f| are gauge integrable.
The definition of the gauge integral is also much simpler than the Lebesgue integral, as can be seen in this presentation, An Introduction to the Gauge Integral.