P-filters and hereditary Baire function spaces

We extend the results of Gulʹko and Sokolov proving that a filter F on ω, regarded as a subspace of the Cantor set 2ω, is a hereditary Baire space if and only if F is a nonmeager (i.e., second category) P-filter. We also prove related results on hereditary Baire spaces of continuous functions Cp(X).