From an arbitrary convergent sequence of sets of bounded variation we can select a subsequence such that there is convergence in almost every hyperplane.
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A. G. Vitushkin, Multidimensional Variations of Sets [in Russian], Moscow (1954).
Translated from Matematicheskie Zametki, Vol. 15, No. 4, pp. 521–526, April, 1974.
The author thanks A. G. Vitushkin and M. S. Mel'nikov for their constant interest in his work.
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Meilanov, V.S. Sequences of closed sets of bounded variation converging in the deviation metric. Mathematical Notes of the Academy of Sciences of the USSR 15, 305–308 (1974). https://doi.org/10.1007/BF01095118
- Convergent Sequence
- Arbitrary Convergent Sequence