Geodesic
Compactness criteria for spaces of measurable functions
Algebra i analiz, Tome 26 (2014) no. 1, pp. 68-93.

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The paper contains new compactness criteria for a wide class of translation-invariant spaces of measurable functions. The results imply new compactness theorems for the families of Orlicz classes (such as $L_0(\mathbb R^d)$) and Marcinkiewicz–Lorentz spaces (including $L_{pq}$ with $p1$).
Keywords: compactness, translation invariant $F$- and $B$-lattices, Orlicz classes, Marcinkiewicz–Lorentz quasi-Banach spaces. 
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Yu. Brudnyi. Compactness criteria for spaces of measurable functions. Algebra i analiz, Tome 26 (2014) no. 1, pp. 68-93. http://geodesic.mathdoc.fr/item/AA_2014_26_1_a2/

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