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### Abstract

We formalize the Riesz-Markov-Kakutani representation theorem following pp.37-47 of the book

*Real and Complex Analysis*by Rudin. This entry also includes formalization of regular measures, tightness of measures, and Urysohn's lemma on locally compact Hausdorff spaces. Roughly speaking, the theorem states that if $\varphi$ is a positive linear functional from $C(X)$ (the space of continuous functions from $X$ to complex numbers which have compact supports) to complex numbers, then there exists a unique measure $\mu$ such that for all $f\in C(X)$, \[\varphi(f) = \int f \mathrm{d}\mu.\]