Hausdorff compactifications and lebesgue sets
β Scribed by Jose L. Blasco
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 409 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0166-8641
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We characterize in terms of Hausdorff measures and descriptive complexity subsets M Δ± R which are (1) the image under some C n function f of the set of points where derivatives of first n orders are zero, (2) the set of points where the level sets of some C n function are perfect, and (3) the set
Periodic orbits and zeta functions are used to compute the rate of escape from Julia sets and their Hausdorff dimension for the one parameter family of complex analytic maps z --) z'? + c. The results are compared with the perturbative expansions of Widom et al. [/. Sfut. Phys. 32, 443 (1983)].
It is proved that every bounded infinite set in a weakly compactly determined Banach space contains a subset minimal for the Hausdorff measure of noncompactness whose measure is the same as the measure of the whole set. Various coefficients related to minimal sets are also studied.