  We provide new simple proofs of the Kolmogorov extension theorem and
Prokhorovs' theorem. The proof of the Kolmogorov extension theorem is based on
the simple observation that $\mathbb{R}$ and the product measurable space
$\{0,1\}^\mathbb{N}$ are Borel isomorphic. To show Prokhorov's theorem, we
observe that we can assume that the underlying space is
$\mathbb{R}^\mathbb{N}$. Then the proof of Prokhorov's theorem is a
straightforward application of the Kolmogorov extension theorem we just proved.
