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In this paper, we investigate compact ultrametric measure spaces which form a subset $\mathcal{U}^w$ of the collection of all metric measure spaces $\mathcal{M}^w$.
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Tam Le, Nhat Ho, and Makoto Yamada · 1910
Earlier work this paper cites.
On the translocation of masses, cr (dokl.) acad
Leonid V. Kantorovich · 1942
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About level sets of continuous functions with partial derivatives
Georgy M. Adelson-Velskii and Aleksandr S. Kronrod · 1945
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Sur les points singuliers d’une forme de pfaff completement integrable ou d’une fonction numerique [on the singular points of a completely integrable pfaff form or of a numerical function]
Georges Reeb · 1946
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Elements of the theory of functions and functional analysis , volume 1
Andreĭ N. Kolmogorov and Sergeĭ V. Fomin · 1957
Earlier work this paper cites.
On a space of completely additive functions (russ.)
Leonid V. Kantorovich and G Rubinstein · 1958
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