# The Riesz-Markov-Kakutani Representation Theorem

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...