I am looking for a reference to the following result. 



> 
> Let $f:\mathbb R^m\to\mathbb R$ be a convex function.
>  Then $f$ is differentiable at all points of outside of a countable union of $(m-1)$-rectifiable sets.
> 
> 
> 


**Comments:**


* $n$-rectifiable set is an image of Lipschitz map from bounded domain in $\mathbb R^n$
* I checked Federer's *"Geometric Measure Theory"*, but I might miss the right place.
* **Extract from the Greg's answer** *(for those who are lazy to read the paper):* In [this paper](http://dml.cz/dmlcz/101616), it is given a complete characterization of subsets of nondifferatiable points of a convex function. Namely, it is proved that $A$ is a such a set if and only if it can be covered by countably many graphs of DC-functions. ("DC-function" = "Difference of Convex functions".)



The set of non-smooth points of a convex function is (m - 1)-rectifiable
The paper [On the differentiation of convex functions in finite and infinite dimensional spaces](http://dml.cz/dmlcz/101616) by Zajíček primarily deals with the general question in Banach space, but it looks like it has a summary of the situation (as of 1979) that tells you everything that you might want to know. It has references to closer papers by Anderson-Klee and Besicovitch.


I just Googled around and eventually got to this paper.


