The Measurable and the Non-measurable

Measurable Utility and the Measurable Choice Theorem

The Measurable Kesten Theorem

We give an explicit bound on the spectral radius in terms of the densities of short cycles in finite d-regular graphs. It follows that the a finite d-regular Ramanujan graph G contains a negligible number of cycles of size less than c log log |G|. We prove that infinite d-regular Ramanujan unimodular random graphs are trees. Through Benjamini-Schramm convergence this leads to the following rigi...

K without the measurable

We show in ZFC that if there is no proper class inner model with a Woodin cardinal, then there is an absolutely definable core model that is close to V in various ways. §1. The main theorem. If the universe V of sets does not have within it very complicated canonical inner models for large cardinal hypotheses, then it has a canonical inner model K that in some sense is as large as possible. K i...

Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

Measurable Transformations