On a criterion of the compactness in the space \(L_p. \). (English. Ukrainian original) Zbl 0940.46014

Buldygin, V. V.; Shurenkova, A. V.

Theory Probab. Math. Stat. 52, 33-37 (1996); translation from Teor. Jmovirn. Mat. Stat. 52, 32-36 (1995).

Let \(E \subset L_p(D)\), \(1<p<\infty.\) The analogue of the Kolmogorov theorem of relative compactness of \(E\) in \(L_p(D)\) is proved. A wide class of averaging kernels is considered.

Reviewer: A.Ya.Olenko (Kyïv)

MSC:

46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B50	Compactness in Banach (or normed) spaces

Keywords:

relative compactness; averaging kernel; Kolmogorov theorem