*Published Paper*

**Inserted:** 6 may 2011

**Last Updated:** 2 jul 2013

**Journal:** Calc. Var.

**Volume:** 49

**Pages:** 347-354

**Year:** 2012

**Notes:**

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.
In this short note we ask to what extent the scalar curvature
is constant if the traceless Ricci tensor is assumed to
be *small* rather than identically zero. In particular,
we provide an optimal $L^2$ estimate under suitable assumptions
and show that these assumptions cannot be removed.