Almost orthogonally additive functions

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