A new Cartantype property and strict quasicoverings when P = 1 in metric spaces
Lahti, P. (2018). A new Cartantype property and strict quasicoverings when P = 1 in metric spaces. Annales Academiae Scientiarum Fennicae Mathematica, 43, 10271043. doi:10.5186/AASFM.2018.4364
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Annales Academiae Scientiarum Fennicae MathematicaAuthors
Date
2018Discipline
MatematiikkaCopyright
© The Author & Academia Scientiarum Fennica, 2018.
In a complete metric space that is equipped with a doubling measure and supports
a Poincaré inequality, we prove a new Cartantype property for the fine topology in the case p =
1. Then we use this property to prove the existence of 1finely open strict subsets and strict
quasicoverings of 1finely open sets. As an application, we study fine Newton–Sobolev spaces in the
case p = 1, that is, Newton–Sobolev spaces defined on 1finely open sets.
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Suomalainen tiedeakatemiaISSN Search the Publication Forum
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