Rufus Lawrence

In this talk I will sketch some of the ideas laid out in Alex Simpson's article Measure, randomness and sublocales. We define locales and measures on locales, and give some examples. We then use this formalism to extend the Lebesgue measure to all subsets of $\mathbb{R}^n$. We then show how this does not contradict the apparent existence of "non-measurable" sets, and "resolve" Tarski's paradox.