# Lipschitz functions on the infinite-dimensional torus

@inproceedings{Faifman2014LipschitzFO,
title={Lipschitz functions on the infinite-dimensional torus},
author={Dmitry Faifman and Bo'az Klartag},
year={2014}
}
We discuss the spectrum phenomenon for Lipschitz functions on the infinite-dimensional torus. Suppose that $f$ is a measurable, real-valued, Lipschitz function on the torus $\mathbb{T}^{\infty}$. We prove that there exists a number $a \in \mathbb R$ with the following property: For any $\epsilon > 0$ there exists a parallel, infinite-dimensional subtorus $M \subseteq \mathbb T^{\infty}$ such that the restriction of the function $f-a$ to the subtorus $M$ has an $L^{\infty}(M)$-norm of at most… CONTINUE READING
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