Measurable orthogonally additive functions modulo a discrete subgroup

Abstract

Under appropriate conditions on Abelian topological groups G and H, an orthogonality ⊥ ⊂ G 2 and a σ-algebra \( \mathfrak{M} \) of subsets of G we decompose an \( \mathfrak{M} \)-measurable function f: G → H which is orthogonally additive modulo a discrete subgroup K of H into its continuous additive and continuous quadratic part (modulo K).