О СУЩЕСТВОВАНИИ ИНВАРИАНТНЫХ МЕР НА ТОПОЛОГИЧЕСКИХ АБЕЛЕВЫХ                   n-АРНЫХ ПОЛУГРУППАХ С СОКРАЩЕНИЯМИ

D V Sergeeva

Authors

D. V. Sergeeva Vologda Institute of Law and Economics of the Federal Penal Service

Keywords:

topological n-ary semigroup, n-ary semigroup with reductions, invariant measure

Abstract

Existence of an invariant measure on topological groups and semigroups plays an essential role in creation of the harmonious analysis on similar objects. The similar situation is traced for topological n-ary groups and n-ary semigroups. In this work the necessary and sufficient condition of existence of an invariant measure on topological Abelian n-ary semigroups with reductions is given.

Author Biography

D. V. Sergeeva, Vologda Institute of Law and Economics of the Federal Penal Service

References

Мухин В. В., Сергеева Д. В. Характеры абелевых n-арных полугрупп, обладающих нейтральной последовательностью // Вестник ИжГТУ. – 2010. – № 4. – С. 156–158.

Mukhin V. V. Invariant Measures on Topological Semigroups which have an Ideal wich Open Translation Mappings // Semigroup Forum. – 2001. – Vol. 62. – P. 159–172.

Мухин В. В. Инвариантные меры на топологических n-полугруппах // Весцi нацыянальной акадэмii навук Беларусi. Серыя фiз-матем. навук. – 2000. – № 4. – С. 16–21.