Almost orthogonally additive functions

If a function ff, acting on a Euclidean space RnRn, is “almost” orthogonally additive in the sense that f(x+y)=f(x)+f(y)f(x+y)=f(x)+f(y) for all (x,y)∈⊥∖Z(x,y)∈⊥∖Z, where ZZ is a “negligible” subset of the (2n−1)(2n−1)-dimensional manifold ⊥⊂R2n⊥⊂R2n, then ff coincides almost everywhere with some orthogonally additive mapping.