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Higher Moments of Banach Space Valued Random Variables

Svante Janson Uppsala University, Sweden
Sten Kaijser Uppsala University, Sweden
Available Formats:
Electronic ISBN: 978-1-4704-2617-0
Product Code: MEMO/238/1127.E
List Price: $80.00 MAA Member Price:$72.00
AMS Member Price: $48.00 Click above image for expanded view Higher Moments of Banach Space Valued Random Variables Svante Janson Uppsala University, Sweden Sten Kaijser Uppsala University, Sweden Available Formats:  Electronic ISBN: 978-1-4704-2617-0 Product Code: MEMO/238/1127.E  List Price:$80.00 MAA Member Price: $72.00 AMS Member Price:$48.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 2382015; 110 pp
MSC: Primary 60; Secondary 46;

The authors define the $k$:th moment of a Banach space valued random variable as the expectation of its $k$:th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space.

The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Moments of Banach space valued random variables
• 4. The approximation property
• 5. Hilbert spaces
• 6. $L^p(\mu )$
• 7. $C(K)$
• 8. $c_0(S)$
• 9. $D[0,1]$
• 10. Uniqueness and Convergence
• A. The Reproducing Hilbert Space
• B. The Zolotarev Distances
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Volume: 2382015; 110 pp
MSC: Primary 60; Secondary 46;

The authors define the $k$:th moment of a Banach space valued random variable as the expectation of its $k$:th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space.

The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Moments of Banach space valued random variables
• 4. The approximation property
• 5. Hilbert spaces
• 6. $L^p(\mu )$
• 7. $C(K)$
• 8. $c_0(S)$
• 9. $D[0,1]$
• 10. Uniqueness and Convergence
• A. The Reproducing Hilbert Space
• B. The Zolotarev Distances
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