The Baire Property for the Space of Mappings of the First Functional Lebesgue Class

In this paper, we study the Baire property of the space K₁(X,M) , that is, the mappings of the first functional Lebesgue class, where M is a compact space. We study the class compact spaces for which the Baire property of the space K₁(X,\0,1\) is equivalent to the Baire property of the space K₁(X,M) for any M from this class. We prove that this class contains π -monolithic compacta. In particular, a necessary and sufficient condition is obtained for the space X under which the space K₁(X,G) is Baire for any compact topological group G .