Representation Theorems
Abstract
The Radon Nikodym theorem is reviewed. Vector measures are discussed. Next, the dual spaces of various L p spaces are described as is the dual space of C 0 ( X ) for X a locally compact Hausdorff space. Finally the easier of the Clarkson’s inequalities and a duality argument are used to obtain the Riesz Representation theorem for L p with no assumption that the measure is σ finite.
Fields of Study & Subjects
Advanced Banach Space Theory
Holomorphic and Operator Theory
Random Matrices and Applications
Publication details
- Journal / source
- Chapman & Hall/CRC eBooks
- Pages
- 252–283
- Publication date
- 10 January 2026
- Language
- EN
- Document type
- Book chapter