HIGHLIGHTS
- who: James Camacho Jr. from the New Jersey City University, Kennedy Boulevard, Jersey City, NJ, USA have published the paper: Slightly Regular Measures and Measureable Sets, in the Journal: (JOURNAL) of 13/07/2016
SUMMARY
The authors say that ℓ is a ?-lattice if ⋂? ? ? ∈ ℓ whenever ? ? ∈ ℓ. ??? ≤ ??. Note if ? ∈ ?? (ℓ), the authors have ? ≤ ?? (ℓ), for ? ∈ ??(ℓ); then, ??=?(ℓ? ), and if ? ∈ ??? (ℓ), then ??=?(ℓ). The authors also have for the two outer measures ? ∈ ?? (ℓ) ⊆ ?(ℓ) if ?(?? )=sup{?? (?) | ? ⊆ ??, ? ∈ ℓ} for ? ∈ ℓ and ? ∈ ?V (ℓ) ⊆ ?? (ℓ) if ?(?? )=sup{??? (?) | ? ⊆ ??, ? ∈ ℓ} for ? ∈ ℓ. So sup ](? ? ) ≤ ?(?) and it follows that inf ?(? ? ) ≤ inf ](? ? ) ≤ sup ](? ? ) ≤ ?(?) as ? ≤ ](ℓ). Using ?, ] ∈ ?? (ℓ), the authors get ?(?) ≤ ](?) ≤ sup ](? ? ) ≤ ?(?) as inf ?(? ? )=?(?) and inf ](? ? )=](?). ?? (?) ≤ ?? (?) ≤ sup{? (⋂1 ? ? ), ⋂ ? ? ⊂ ?, | ? ? ∈ ℓ} ≤ ??? (?) ≤ ?? (?)=?? (?) as . . .
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