Non-pathological representation of an Fσ P-ideal

Determine whether, whenever an Fσ ideal is represented as Exh(ϕ) for a lower semicontinuous submeasure ϕ, the representing submeasure can be replaced by a non-pathological lower semicontinuous submeasure ψ satisfying Exh(ϕ)=Exh(ψ)=FIN(ψ).

Background

Solecki’s representation gives an Fσ ideal I=Exh(ϕ)=FIN(ψ) for another lower semicontinuous submeasure ψ. The unresolved issue is whether ψ can preserve non-pathology when the original submeasure ϕ is non-pathological.