On orthogonally exponential and orthogonally additive mappings

Let $E$ be a real inner product space, $(F,+)$ an abelian $\sigma$-bounded topological group, and $K$ a discrete subgroup of $F$. It is proved that (under suitable assumptions on $E)$ the Christensen and Baire measurable orthogonally additive functions $g\colon E\to F/K$ have particular selections. In consequence, descriptions of measurable orthogonally exponential complex functionals on $E$ are obtained.