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Normability of Boolean algebras with a continuous exterior measure. (English. Russian original) Zbl 0466.28005

Sib. Math. J. 21, 645-648 (1981); translation from Sib. Mat. Zh. 21, 216-220 (1980).

MSC:

28A60 Measures on Boolean rings, measure algebras
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
46A40 Ordered topological linear spaces, vector lattices
28A12 Contents, measures, outer measures, capacities

Citations:

Zbl 0029.20401
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Full Text: DOI

References:

[1] D. Maharam, ?An algebraic characterization of measure algebras,? Ann. Math.,48, No. 1, 154-167, (1947). · Zbl 0029.20401 · doi:10.2307/1969222
[2] B. Z. Vulikh, Introduction to the Theory of Partially Ordered Spaces, Gordan and Breach (1967). · Zbl 0186.44601
[3] D. A. Vladimirov, Boolean Algebras [in Russian], Nauka, Moscow (1969).
[4] A. G. Poroshkin, ?Some properties of weak countable distributivity of lattices,? Sib. Mat. Zh.,19, No. 1, 235 (1978). · Zbl 0409.60022 · doi:10.1007/BF00970505
[5] N. Dinculeanu, Vector Measures, Berlin (1966).
[6] A. G. Poroshkin, ?Two properties of Boolean algebras with a vector measure,? Sib. Mat. Zh.,16, No. 2, 336-346 (1975).
[7] V. A. Popov, ?Properties of the ?-integral,? Uch. Zap. Leningr. Pedagog. Inst. im. A. I. Gertsena,541, 3-6 (1972).
[8] A. G. Poroshkin and V. N. Isakov, ?On integrals with respect to an exterior measure,? in: Set Functions [in Russian], Syktyvkar (1977), pp. 5-16.
[9] A. A. Gol’dberg, ?Integrals with respect to semiadditive measures and applications to the theory of entire functions. I,? Mat. Sb.,58, No. 3 288-310 (1962).
[10] G. G. Lorentz, ?Multiply subadditive functions,? Can. J. Math.,4, 455-462 (1952). · Zbl 0047.05903 · doi:10.4153/CJM-1952-041-4
[11] V. A. Popov, ?Existence of additive minorants,? in: Proc. Sixth Komi Republic Youth Conference in the Sciences [in Russian] Syktyvkar (1974), pp. 99-100.
[12] K. Yosida, Functional Analysis, Springer-Verlag, New York. · Zbl 0126.11504
[13] V. A. Popov, ?Additive and semiadditive functions on Boolean algebras,? Sib. Mat. Zh.,17, No. 2, 331-339 (1976). · Zbl 0354.28013
[14] V. N. Aleksyuk, ?A theorem on minorants. Countability of the Maharam problem,? Mat. Zametki,21, No. 5, 597-604 (1977).
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