Krivine's Function Calculus and Bochner Integration
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, cilt.62, sa.3, ss.663-669, 2019 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 62 Sayı: 3
- Basım Tarihi: 2019
- Doi Numarası: 10.4153/s0008439518000036
- Dergi Adı: CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.663-669
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- İstanbul Kültür Üniversitesi Adresli: Evet
Özet
We prove that Krivine's Function Calculus is compatible with integration. Let (Omega, Sigma, mu) be a finite measure space, X a Banach lattice, x epsilon X-n, and f : R-n x Omega -> R a function such that f(., w) is continuous and positively homogeneous for every w E 12, and f (s, ") is integrable for every s E R. Put F(s) = f f (s, w) d (w) and define F(x) and f (x, w) via Krivine's Function Calculus. We prove that under certain natural assumptions F(x) = f f (x, w) d (w), where the right hand side is a Bochner integral.