대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제62권1호
  • /
  • Pages.81-89
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  • 2025
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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DISTAL MEASURES FOR SEMIGROUP ACTIONS

  • Dongkui Ma (School of Mathematics South China University of Technology) ;
  • Yanjie Tang (School of Mathematics South China University of Technology)
  • 투고 : 2024.01.23
  • 심사 : 2024.07.31
  • 발행 : 2025.01.31
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초록

We introduce the notion of distal measure of a semigroup action ϕ on a compact metric space X, and show that the set of distal measures of ϕ is a Gδσ subset of the space 𝓜(X) of Borel probability measures on X with the weak* topology. Moreover, we prove that the distal measures of ϕ with full support is dense in 𝓜(X) under a suitable condition.

키워드

과제정보

The authors really appreciate the referees' valuable remarks and suggestions which helped a lot. YT was partially supported by China Scholarship Council (CSC) grant funded by the Ministry of Education of the P. R. China (No. 202306150095). A part of the paper was completed when YT was visiting the Sejong Institute for Mathematical Sciences (SIMS) from September 19, 2023 to September 18, 2024, she would like to thank the members in SIMS for their hospitality and support.

참고문헌

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