| Popis: |
Let X be a set and A ⊆ P ( X ) be a family closed under finite intersections such that ∅ , X ∈ A . If ψ = o , ω , γ , then Ψ ( A ) is the family of those ψ-covers U for which U ⊆ A . In [3] , properties ( Ψ 0 ) of a family F ⊆ X R of real functions have been introduced. The main result of the paper Theorem 4.1 reads as follows: if Φ = Ω , Γ and Ψ = O , Ω , Γ , then for any pair 〈 Φ , Ψ 〉 different from 〈 Ω , O 〉 , X has the covering property S 1 ( Φ ( A ) , Ψ ( A ) ) if and only if the family of non-negative upper A -semimeasurable real functions satisfies the selection principle S 1 ( Φ 0 , Ψ 0 ) . Similarly for S fin and U fin . Some related results are also presented. |
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