اندازه‌های پایای عمل گروه‌های میانگین‌پذیر و آنتروپی آن‌ها

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه ریاضی، دانشکده علوم پایه، دانشگاه صنعتی جندی شاپور دزفول، ایران

2 گروه ریاضی، دانشکده علوم پایه، دانشگاه صنعتی جندی شاپور دزفول، ایران‎

3 گروه مهندسی برق، واحد تهران مرکز، دانشگاه آزاد اسلامی، تهران، ایران

چکیده

در این مقاله، به کمک مفهوم اندازۀ قطری، یک تابع اطلاعات برای عمل گروه میانگین‌پذیر بر یک فضای متریک فشرده تعریف کرده و سپس آنتروپی عمل گروه را از آن به‌ دست می‌آوریم. به‌عبارت‌دیگر، نشان می‌دهیم که انتگرال از تابع اطلاعات تعریف‌شده نسبت به اندازۀ ‌ قطری برابر با آنتروپی عمل گروه میانگین‌پذیر خواهد شد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Invariant measures of action of amenable groups and their entropy

نویسندگان [English]

  • Alireza Alehafttan 1
  • Hossein Kasiri 2
  • Mehran Hosseinzadeh Dizaj 3
1 Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran
2 Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran
3 Department of Electrical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran
چکیده [English]

In this article, with the help of the concept of diagonal measure, we define an information function for the amenable group action on a compact metric space and then obtain the entropy of the group action from it. In other words, we show that the integral of the defined information function will be equal to the entropy of the amenable group action.

کلیدواژه‌ها [English]

  • ‎Amenable group
  • Folner sequence
  • Information function
  • Entropy
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