Geodesic
Compactness principle for periodic singular and fine structures
Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 244-253

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We consider the compactness principle in the variable space $L^2$ related to a periodic Borel measure. We assume that the periodic Borel measure determines a periodic singular or a fine structure. We prove the compactness principle for periodic singular and fine grids, box structures, and composite structures on the plane and in space. 
@article{MZM_2006_79_2_a7,
     author = {V. V. Shumilova},
     title = {Compactness principle for periodic singular and fine structures},
     journal = {Matemati\v{c}eskie zametki},
     pages = {244--253},
     publisher = {mathdoc},
     volume = {79},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a7/}
}
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V. V. Shumilova. Compactness principle for periodic singular and fine structures. Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 244-253. http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a7/