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Weil topology on a group equipped with a measure that is invariant on a subset. (English. Russian original) Zbl 0592.28009

Sib. Math. J. 25, 447-451 (1984); translation from Sib. Mat. Zh. 25, No. 3(145), 132-136 (1984).
A topology on a group equipped with a measure which is initially defined only on a set and satisfies natural conditions is constructed.
Reviewer: A.Grincevičius

MSC:

28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
43A05 Measures on groups and semigroups, etc.
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References:

[1] A. Weil, Integration in Topological Groups and Its Applications [Russian translation], IL, Moscow (1950).
[2] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. I, Die Grundlehren der Mat. Wiss., Band 115, Springer-Verlag, Berlin, Göttingen, Heidelberg (1963). · Zbl 0115.10603
[3] P. Halmos, Measure Theory, Springer-Verlag (1974).
[4] A. D. Aleksandrov, ?On groups with invariant measure,? Dokl. Akad. Nauk SSSR,34, No. 1, 5-9 (1942).
[5] V. V. Mukhin and A. R. Mirotin, ?Weil topology in semigroups with invariant measure,? in: Seventh All-Union Topology Conference [in Russian], Minsk (1977), p. 132.
[6] V. V. Mukhin, ?Invariant measures on semigroups and imbedding of topological semigroups in topological groups,? Mat. Sb.,112, No. 2, 295-303 (1980). · Zbl 0442.28010
[7] P, Halmos, Measure Theory, Springer-Verlag (1974).
[8] A. R. Mirotin and V. V. Mukhin, ?On invariant measures which admit extension from a semigroup to its group of quotients,? Mat. Zametki,24, No. 6, 819-828 (1978). · Zbl 0427.28013
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