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Keywords:
quasigroup; topological IP-loop; Haar measure; content; uniform; space; left-invariant uniformity
quasigroup; topological IP-loop; Haar measure; content; uniform; space; left-invariant uniformity
Summary:
In this paper, we give conditions ensuring the existence of a Haar measure in topological IP-loops.
References:
[1] Baez, J.: The Octonions. Bull. Amer. Math. Soc. 39 (2002), 145–205. DOI 10.1090/S0273-0979-01-00934-X | MR 1886087 | Zbl 1026.17001
[2] Belousov, V. D.: Foundations of the Theory of Quasigroups and Loops (in Russian). Nauka, Moscow, 1967. MR 0218483
[3] Bruck, R. H.: Some results in the theory of quasigroups. Trans. Amer. Math. Soc. 55 (1944), 19–52. MR 0009963 | Zbl 0063.00635
[4] Bruck, R. H.: Contributions to the theory of loops. Trans. Amer. Math. Soc. 60 (1946), 245–354. MR 0017288 | Zbl 0061.02201
[5] Haar, A.: Der Massbegriff in der Theorie der kontinuierlichen Gruppen. Ann. Math. 34 (1933), 147–169. DOI 10.2307/1968346 | MR 1503103 | Zbl 0006.10103
[6] Halmos, P.: Measure Theory. Springer-Verlag New York Inc. 1974. MR 0453532 | Zbl 0283.28001
[7] Hudson, S. N.: Transformation groups in the theory of topological loops. Proc. Amer. Math. Soc. 15 (1964), 872–877. DOI 10.1090/S0002-9939-1964-0167962-X | MR 0167962
[8] Hudson, S. N.: Topological loops with invariant uniformities. Trans. Amer. Math. Soc. 109 (1963), 1, 181–190. DOI 10.1090/S0002-9947-1963-0155302-5 | MR 0155302 | Zbl 0115.02501
[9] Chein, O., Pflugfelder, H. O., Smith, J. D. H.: Quasigroups and Loops. Theory and Application. Heldermann Verlag, 1990. MR 1125806 | Zbl 0719.20036
[10] Kinyon, M. K., Kunen, K., Phillips, J. D.: Every diassociative A-loop is Moufang. Proc. Amer. Math. Soc. 130 (2002), 619–624. DOI 10.1090/S0002-9939-01-06090-7 | MR 1866009 | Zbl 0990.20044
[11] Markechová, D., Stehlíková, B., Tirpáková, A.: The uniqueness of a left Haar measure in topological IP-loops. (Submitted for publication).
[12] Moufang, R.: Zur Struktur von alternativ Korpern. Math. Ann. 110 (1935), 416–430. DOI 10.1007/BF01448037 | MR 1512948
[13] Nagy, P. T., Strambach, K.: Coverings of topological loops. J. Math. Sci. 137 (2006), 5, 5098–5116. DOI 10.1007/s10958-006-0289-1 | MR 2462071 | Zbl 1181.22009
[14] Nagy, P. T., Strambach, K.: Loops in Group Theory and Lie Theory. De Gruyter Expositions in Mathematics, Berlin – New York 2002. MR 1899331 | Zbl 1050.22001
[15] Pflugfelder, H. O.: Quasigroups and Loops. Introduction. Heldermann Verlag, 1990. MR 1125767 | Zbl 0719.20036
[16] Riečan, B., Neubrunn, T.: Integral, Measure and Ordering. Kluwer Academic Publishers 1997. MR 1489521
[17] Schwarz, Š.: On the existence of invariant measures on certain types of bicompact semigroups (in Russian). Czechoslovak Math. J. 7 (1957), 82, 165–182. MR 0089364
[18] Smith, J. D. H.: Quasigroup Representation Theory. Taylor & Francis, 2006.
[19] Weil, A.: Basic Number Theory. Academic Press, 1971.
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