The Riesz-Markov-Kakutani Representation Theorem

1 · Admiraldesvl · Sept. 19, 2020, 12:57 a.m.
This postIs intended to establish the existence of the Lebesgue measure in the future, which is often denoted by $m$. In fact, the Lebesgue measure follows as a special case of R-M-K representation theorem. You may not believe it, but euclidean properties of $\mathbb{R}^k$ plays no role in the existence of $m$. The only topological property that works is the fact that $\mathbb{R}^k$ is a locally compact Hausdorff space.The theorem is named after F. Riesz who introduced it for continuous function...