# Second order partial derivatives of Sobolev functions.

Is it true that $$W^{2,1}_{loc}$$ functions (after possibly modifying them on a set of measure zero) allow classical second order partial derivatives almost everywhere?

The corresponding problem for first order partial derivatives in $$W^{1,1}_{loc}$$ has positive answer by the ACL characterization of Sobolev functions (Nikodym’s theorem). It seems to me that the answer to my question will follow by iteration but all the textbooks that I have checked are suspiciously silent on the topic.