![Open Access](https://i-scholar.in/lib/pkp/templates/images/icons/fulltextgreen.png)
![Restricted Access](https://i-scholar.in/lib/pkp/templates/images/icons/fulltextred.png)
![Open Access](https://i-scholar.in/lib/pkp/templates/images/icons/fulltextgreen.png)
![Open Access](https://i-scholar.in/lib/pkp/templates/images/icons/fulltext_open_medium.gif)
![Restricted Access](https://i-scholar.in/lib/pkp/templates/images/icons/fulltextred.png)
![Restricted Access](https://i-scholar.in/lib/pkp/templates/images/icons/fulltext_restricted_medium.gif)
Pettis-Type Spaces for a Bounded Family of Measures
Subscribe/Renew Journal
Let (Ω,Σ,μ) be a probability space and let N⊂ca (Σ) be a bounded family of positive measures and X be a Banach space. Let P1(N,X) be the Pettis-type spaces with respect to N. Assuming that X is weakly sequentially complete, we prove the completeness of P1(N,X) with respect to the Pettis semi-norm. Also we prove the Vitali’s convergence theorem, Lebesgue dominated theorem and a necessary and sufficient condition for a function to belong to P1(N,X).
Keywords
Lebesgue-Type Spaces, Pettis-Type Spaces, Vitali’s Convergence Theorem, Lebesgue Dominated Convergence Theorem, Young’s Function, Orlicz Spaces.
Subscription
Login to verify subscription
User
Font Size
Information
![](https://i-scholar.in/public/site/images/abstractview.png)
Abstract Views: 201
![](https://i-scholar.in/public/site/images/pdfview.png)
PDF Views: 0