Geodesic
Diameters of classes of continuous functions in the $L_p$ space
Matematičeskie zametki, Tome 10 (1971) no. 5, pp. 493-500.

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In the $L_p(a,b)$ space the exact values of $n$-diameters $(n=1,2,\dots)$ are found of the class $H_\omega[a,b]$ of the functions $f(x)$ such that $|f(x')-f(x'')|\leqslant\omega(|x'-x''|)$, where $\omega(t)$ is a given continuity module which is convex upwards. 
@article{MZM_1971_10_5_a1,
     author = {N. P. Korneichuk},
     title = {Diameters of classes of continuous functions in the $L_p$ space},
     journal = {Matemati\v{c}eskie zametki},
     pages = {493--500},
     publisher = {mathdoc},
     volume = {10},
     number = {5},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_5_a1/}
}
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N. P. Korneichuk. Diameters of classes of continuous functions in the $L_p$ space. Matematičeskie zametki, Tome 10 (1971) no. 5, pp. 493-500. http://geodesic.mathdoc.fr/item/MZM_1971_10_5_a1/