6533b834fe1ef96bd129df5f
RESEARCH PRODUCT
Porous measures on $\mathbb {R}^{n}$: Local structure and dimensional properties
Maarit JärvenpääEsa Järvenpääsubject
Packing dimensionCorollaryApplied MathematicsGeneral MathematicsMathematical analysisRadon measurePorosityUpper and lower boundsLocal structurePhysics::GeophysicsMathematicsdescription
We study dimensional properties of porous measures on R n . As a corollary of a theorem describing the local structure of nearly uniformly porous measures we prove that the packing dimension of any Radon measure on R n has an upper bound depending on porosity. This upper bound tends to n - 1 as porosity tends to its maximum value.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-06-08 | Proceedings of the American Mathematical Society |