Back to Search
Start Over
Gauges for the cookie-cutter sets.
- Source :
- Acta Mathematica Sinica; Dec2009, Vol. 25 Issue 12, p2119-2126, 8p
- Publication Year :
- 2009
-
Abstract
- Let E be a cookie-cutter set with dim<subscript> H</subscript> E = s. It is known that the Hausdorff s-measure and the packing s-measure of the set E are positive and finite. In this paper, we prove that for a gauge function g the set E has positive and finite Hausdorff g-measure if and only if 0 < lim inf<subscript> tâ0</subscript> $$ \tfrac{{g(t)}} {{t^s }} $$ < â. Also, we prove that for a doubling gauge function g the set E has positive and finite packing g-measure if and only if 0 < lim sup<subscript> tâ0</subscript> $$ \tfrac{{g(t)}} {{t^s }} $$ < â. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 25
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 45686601
- Full Text :
- https://doi.org/10.1007/s10114-009-7455-6