The Sharkovskiĭ Theorem for spaces of measurable functions

Diagonal operators on spaces of measurable functions

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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...

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.

On Spaces of Measurable Vector - Valued Functions 399 Proof