| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Nacl Autonoma Mexico, Ctr Ciencias Matemat, Campus Morelia, Apartado Postal 61-3, Morelia, Michoacan - Mexico
[2] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | JOURNAL OF APPLIED ANALYSIS; v. 25, n. 1, p. 25-36, JUN 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
A weak selection on R is a function f : {[}R](2)-> R such that f([x, y]) is an element of (x, y] for each [x, y] is an element of {[}R](2). In this article, we continue with the study (which was initiated in {[}1]) of the outer measures lambda(f) on the real line R defined by weak selections f. One of the main results is to show that CH is equivalent to the existence of a weak selection f for which lambda(f)(A) = 0 whenever vertical bar A vertical bar <= omega and lambda(f) (A) = infinity otherwise. Some conditions are given for a sigma-ideal of R in order to be exactly the family N-f of lambda(f )-null subsets for some weak selection f. It is shown that there are 2(c) pairwise distinct ideals on R of the form N-f, where f is a weak selection. Also, we prove that the Martin axiom implies the existence of a weak selection f such that N-f is exactly the sigma-ideal of meager subsets of R. Finally, we shall study pairs of weak selections which are ``almost equal{''} but they have different families of lambda f-measurable sets. (AU) | |
| FAPESP's process: | 14/16955-2 - Outer measures by weak selections and hyperspaces. |
| Grantee: | Yasser Fermán Ortiz Castillo |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |