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Hotspot Lemmas for Noncompact Spaces

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Notes

  1. We are unaware of a standard term for this structure and have decided on this name in analogy with the definition of semialgebra, which requires a finite disjoint union rather than a countable one. Note that the conditions for being a \(\sigma\)-algebra are stronger than those for being an algebra, while the conditions for being a semi-\(\sigma\)-algebra are weaker than those for being a semialgebra.

References

  1. I. I. Piatetskii-Shapiro, Izv. Akad. Nauk SSSR Ser. Mat. 15 (1), 47 (1951).

    Google Scholar 

  2. A. G. Postnikov, Trudy Mat. Inst. Steklov 82 (1966).

    Google Scholar 

  3. N. G. Moshchevitin and I. D. Shkredov Math. Notes 73 (3–4), 539 (2003).

    Article  MathSciNet  Google Scholar 

  4. A. G. Postnikov, Trudy Mat. Inst. Steklov 57 (1960).

    Google Scholar 

  5. S. Akiyama, H. Kaneko, and D. H. Kim, Generic Point Equivalence and Pisot Numbers, in Ergodic Theory and Dynamical Systems (2019), pp. 1–12.

    Google Scholar 

  6. S. Nandakumar, S. Pulari, P. Vishnoi, and G. Viswanathan, An Analogue of Pillai’s Theorem for Continued Fraction Normality and an Application to Subsequences, arXiv: arXiv:1909.03431 (2019).

    Google Scholar 

  7. J. Vandehey Compos. Math. 153 (2), 274 (2017).

    Article  MathSciNet  Google Scholar 

  8. I. D. Shkredov J. Math. Sci. 182 (4), 567 (2012).

    Article  MathSciNet  Google Scholar 

  9. V. I. Bogachev Measure Theory (Springer, 2007), Vol. II.

    Book  Google Scholar 

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Acknowledgments

The authors wish to thank N. G. Moshchevitin, I. D. Shkredov, and J. Vandehey for helpful discussions about the hotspot lemma, as well as the referee for helpful edits.

Funding

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under grant no. DGE-1656466. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Authors and Affiliations

  1. Princeton University, 08540, Princeton, United States of America

    D. Airey

  2. Uniwersytet im. Adama Mickiewicza w Poznaniu, Collegium Mathematicum, 61-614, Poznań, Poland

    B. Mance

Authors
  1. D. Airey
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  2. B. Mance
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Correspondence to D. Airey.

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Airey, D., Mance, B. Hotspot Lemmas for Noncompact Spaces. Math Notes 108, 434–439 (2020). https://doi.org/10.1134/S0001434620090126

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  • DOI: https://doi.org/10.1134/S0001434620090126

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