Geodesic
Left-invariant measures on topological $n$-ary subsemigroup of binary groups
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 6 (2015), pp. 50-55

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Convolutions of measures and functions, as well as the Fourier transform of measures on locally compact Abelian $n$-ary groups were introduced in [1]. Development of harmonic analysis on $n$-ary algebraic objects endowed with a topology is closely related to the existence of a non-zero invariant measure on such objects. Invariant measures on topological $n$-ary semigroups were considered in [2] and [3]. In Theorem 2 of this paper, we establish necessary and sufficient conditions for the existence of a left-invariant measure on topological $n$-ary subsemigroups of binary groups. It can be treated as an extension of the results of [4] to the case of $n$-ary topological semigroups. The result established in Theorem 1 establishes is interesting for topological algebra.
Keywords: left-invariant measure, topological $n$-ary semigroup, ideal of an $n$-ary semigroup. 
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     author = {D. V. Sergeeva},
     title = {Left-invariant measures on topological $n$-ary subsemigroup of binary groups},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {50--55},
     publisher = {mathdoc},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2015_6_a5/}
}
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D. V. Sergeeva. Left-invariant measures on topological $n$-ary subsemigroup of binary groups. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 6 (2015), pp. 50-55. http://geodesic.mathdoc.fr/item/VTGU_2015_6_a5/