Operator-Valued Measures and Integrals for Cone-Valued Functions (eBook)

Walter Roth (Autor)

eBook Download: PDF

2009 | 2009
X, 356 Seiten
Springer Berlin (Verlag)
9783540875659 (ISBN)

Infos

Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions, but different approaches are used for each case. This book develops a general theory of integration that simultaneously deals with all three cases.

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Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions. Different approaches are applied in each of these cases using different techniques. The order structure of the (extended) real number system is used for real-valued functions and measures whereas suprema and infima are replaced with topological limits in the vector-valued case.
A novel approach employing more general structures, locally convex cones, which are natural generalizations of locally convex vector spaces, is introduced here. This setting allows developing a general theory of integration which simultaneously deals with all of the above-mentioned cases.

Inhalt

Locally Convex Cones.- Measures and Integrals. The General Theory.- Measures on Locally Compact Spaces.

Produkt-Details

• Reihe/Serie: Lecture Notes in Mathematics
• Verlagsort: Berlin
• Sprache: englisch
• Schlagworte: 28B20, 46A13, 46E40, 46G10 • Boundary element method • Compact space • Cone-valued functions • DEX • Integral • integral representation • Integration • Integration Theory • Locally Convex Cones • NATURAL • real number • System • techniques • Vector Space • Vector-valued measures
• ISBN-13: 9783540875659 / 9783540875659