6533b7d7fe1ef96bd126915d
RESEARCH PRODUCT
Local dimensions of sliced measures and stability of packing dimensions of sections of sets
Marta LlorenteMaarit JärvenpääEsa Järvenpääsubject
CombinatoricsSection (fiber bundle)Mathematics(all)Packing dimensionDimension (vector space)Plane (geometry)General MathematicsHausdorff dimensionMathematical analysisConstant (mathematics)Stability (probability)Mathematicsdescription
Abstract Let m and n be integers with 0 R n to certain properties of plane sections of μ. This leads us to prove, among other things, that the lower local dimension of (n−m)-plane sections of μ is typically constant provided that the Hausdorff dimension of μ is greater than m. The analogous result holds for the upper local dimension if μ has finite t-energy for some t>m. We also give a sufficient condition for stability of packing dimensions of section of sets.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2004-03-01 | Advances in Mathematics |