Geodesic
Extension of quasi-Lipschitz set functions
Matematičeskie zametki, Tome 17 (1975) no. 1, pp. 21-31.

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In this article we consider so-called $\mathscr N$-triangular and quasi-Lipschitz set functions. In terms of $\mathscr N$ -semimeasures, we establish necessary and sufficient conditions for extending a quasi-Lipschitz set function which is continuous from above at zero from a ring of sets to the $\sigma$-ring generated by these sets, and also conditions for the uniqueness of the extension. As simple corollaries we obtain analogous results for vector-valued measures, continuous triangular measures, and real-valued finite $\mathscr N$ -triangular set functions which are continuous from above at zero. 
@article{MZM_1975_17_1_a2,
     author = {N. S. Gusel'nikov},
     title = {Extension of {quasi-Lipschitz} set functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {21--31},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_1_a2/}
}
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N. S. Gusel'nikov. Extension of quasi-Lipschitz set functions. Matematičeskie zametki, Tome 17 (1975) no. 1, pp. 21-31. http://geodesic.mathdoc.fr/item/MZM_1975_17_1_a2/