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Some remarks on the Steinhaus property for invariant extensions of the Lebesgue measure

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Abstract

A translation invariant measure on the real line R is constructed, which extends the Lebesgue measure on R and for which the Steinhaus property fails in a strong form.

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Acknowledgements

The author is grateful to the referees for their useful comments and suggestions.

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  1. A. Razmadze Mathematical Institute, Tamarashvili Str., 6, 0177, Tbilisi, Georgia

    Alexander Kharazishvili

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  1. Alexander Kharazishvili
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Kharazishvili, A. Some remarks on the Steinhaus property for invariant extensions of the Lebesgue measure. European Journal of Mathematics 5, 81–90 (2019). https://doi.org/10.1007/s40879-017-0211-z

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