Editing Weak derivative (section)

== Properties ==

If two functions are weak derivatives of the same function, they are equal except on a set with [[Lebesgue measure]] zero, i.e., they are equal [[almost everywhere]].  If we consider [[equivalence classes]] of functions such that two functions are equivalent if they are equal almost everywhere, then the weak derivative is unique.

Also, if ''u'' is differentiable in the conventional sense then its weak derivative is identical (in the sense given above) to its conventional (strong) derivative.  Thus the weak derivative is a generalization of the strong one.  Furthermore, the classical rules for derivatives of sums and products of functions also hold for the weak derivative.