sigma-idea s and outer measures on the real line

Autor(es)

Garcia-Ferreira, Salvador ^[1] ; Tomita, Artur H. ^[2] ; Ortiz-Castillo, Yasser Ferman ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF APPLIED ANALYSIS; v. 25, n. 1, p. 25-36, JUN 2019.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 14/16955-2 - Medidas exteriores por seleções fracas e hiperespaços.
• Beneficiário: Yasser Fermán Ortiz Castillo
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado