In this paper we give sufficient conditions for the precompactness of sets in general global Morrey-type spaces GMp_(θ,w(.))(R~n). In the case θ= ∞, it follows the result for the generalized Morrey spaces {formula}, and for w(r)= r~(-λ), 0= ∞, {formula} there follows the known result for the Morrey spaces {formula}. In the case A= 0 this is the well-known Frechet-Kolmogorov theorem. The pre-compactness of sets in Morrey spaces was investigated in many works, and in generalized Morrey spaces {formula} in our previous works. The aim of this paper is to generalize these results to the case of general global Morrey-type spaces GMpθ,w(.)(Rn).
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