On a class of singular measures satisfying a strong annular decay condition
Copyright policy )On a class of singular measures satisfying a strong annular decay condition
A metric measure space ( X , d , μ ) (X, d, \mu ) is said to satisfy the strong annular decay condition if there is a constant C > 0 C>0 such that μ ( B ( x , R ) ∖ B ( x , r ) ) ≤ C R − r R μ ( B ( x , R ) ) \begin{equation*} \mu \big ( B(x, R) \setminus B(x,r) \big ) \leq C\, \frac {R-r}{R}\, \mu (B(x,R)) \end{equation*} for each x ∈ X x\in X and all 0 > r ≤ R 0>r \leq R . If d ∞ d_{\infty } is the distance induced by the ∞ \infty -norm in R N \mathbb {R}^N , we construct examples of singular measures μ \mu on R N \mathbb {R}^N such that ( R N , d ∞ , μ ) (\mathbb {R}^N, d_{\infty }, \mu ) satisfies the strong annular decay condition.
- Autonomous University of Barcelona Spain
- University of Jyväskylä Finland
- University of Barcelona Spain
- University of Alicante Spain
Length, area, volume, other geometric measure theory, ta111, metriset avaruudet, Metric measure spaces, Bernoulli product, funktioteoria, metric measure space, singular measure, Doubling measure, Analysis on metric spaces, Mathematics - Metric Geometry, annular decay condition, doubling measure, doubling property, Matematiikka, Annular decay condition, mittateoria, Mathematics
Length, area, volume, other geometric measure theory, ta111, metriset avaruudet, Metric measure spaces, Bernoulli product, funktioteoria, metric measure space, singular measure, Doubling measure, Analysis on metric spaces, Mathematics - Metric Geometry, annular decay condition, doubling measure, doubling property, Matematiikka, Annular decay condition, mittateoria, Mathematics
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