Geodesic
The Brooks--Jevett theorem on uniform dimentricularity on a non-sigma-full class of sets
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 4 (2017), pp. 33-39

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For a sequence of exhaustive composition-triangular set functions defined on a non-sigma-complete class of sets, more general than the ring of sets, the Brooks–Jewett theorem on uniform exhaustibility is proved. As a corollary, we have obtained analogue of the Brooks–Jewett theorem for functions defined on a sigma-summable class of sets. It is shown that if, in addition to the property compositional triangularity, the set functions have the composite semi-additivity property and are continuous from above at zero, then an analog of Nikodym's theorem on equicontinuous weak continuity is valid for them. The corresponding results are obtained for a family of quasi-Lipschitz set functions.
Keywords: composition-triangular set functions, composition-semi-additive set functions, non-sigmacomplete class of sets, exhaustibility, continuity from above at zero, uniform exhaustibility, equicontinuous weak continuity.
Mots-clés : multiplicative class of sets 
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     title = {The {Brooks--Jevett} theorem on uniform dimentricularity on a non-sigma-full class of sets},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {33--39},
     publisher = {mathdoc},
     number = {4},
     year = {2017},
     language = {ru},
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T. A. Sribnaya. The Brooks--Jevett theorem on uniform dimentricularity on a non-sigma-full class of sets. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 4 (2017), pp. 33-39. http://geodesic.mathdoc.fr/item/VSGU_2017_4_a3/