Daniell integral

Summary

The Daniell integral is an approach to integration that starts from a positive linear functional on a space of elementary functions. It does not start from a measure. The functional must satisfy a continuity condition along decreasing sequences. It then extends to a large class of integrable functions, and the measure of a set appears afterwards as the integral of its indicator function. This approach gives the Lebesgue integral and integrals on locally compact spaces in one framework.