*Published Paper*

**Inserted:** 6 may 2011

**Last Updated:** 27 jun 2019

**Journal:** Calc. Var.

**Volume:** 49

**Pages:** 347-354

**Year:** 2012

For the update version and eventual errata see the webpage http:/www.math.uzh.ch*delellis*

**Abstract:**

Schur's lemma states that every Einstein manifold of dimension $n\geq 3$ has constant scalar curvature. Here $(M,g)$ is defined to be Einstein if its traceless Ricci tensor $$\Rico:=\Ric-\frac{R}{n}g$$ is identically zero. In this short note we ask to what extent the scalar curvature is constant if the traceless Ricci tensor is assumed to be \emph{small} rather than identically zero.