Geodesic
Waterman classes and piecewise monotone approximations
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2009), pp. 46-48

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A neсessary and sufficient condition for a class of functions with a given estimate on piecewise monotone approximations to be embedded into the Waterman class (of functions of bounded $\Lambda$-variation) is obtained. 
@article{VMUMM_2009_6_a7,
     author = {A. N. Bakhvalov},
     title = {Waterman classes and piecewise monotone approximations},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {46--48},
     publisher = {mathdoc},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2009_6_a7/}
}
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A. N. Bakhvalov. Waterman classes and piecewise monotone approximations. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2009), pp. 46-48. http://geodesic.mathdoc.fr/item/VMUMM_2009_6_a7/