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 -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.
A. V. Osipov (Mon,) studied this question.