Differentiation of measures on a non-separable space, and the Radon-Nikodym theorem

Oleksii Mostovyi, Pietro Siorpaes

Given positive measures $\nu ,\mu$ on an arbitrary measurable space $(\Omega ,\mathcal{F})$, we construct a sequence of finite partitions $({\pi }_n{)}_n$ of $(\Omega ,\mathcal{F})$ s.t. $$ \sum_{A\in π_n…