The Choquet and Kellogg properties for the fine topology when p=1 in metric spaces
Lahti, P. (2019). The Choquet and Kellogg properties for the fine topology when p=1 in metric spaces. Journal de Mathematiques Pures et Appliquees, 126, 195-213. doi:10.1016/j.matpur.2019.01.004
Published inJournal de Mathematiques Pures et Appliquees
© 2019 Elsevier Masson SAS.
In the setting of a complete metric space that is equipped with a doubling measure and supports a Poincar´e inequality, we prove the fine Kellogg property, the quasi-Lindel¨of principle, and the Choquet property for the fine topology in the case p = 1. Dans un contexte d’espace m´etrique complet muni d’une mesure doublante et supportant une in´egalit´e de Poincar´e, nous d´emontrons la propri´et´e fine de Kellogg, le quasi-principe de Lindel¨of, et la propri´et´e de Choquet pour la topologie fine dans le cas p = 1.
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