Measure Theory

J.L. Doob (Autor)

Buch | Softcover

212 Seiten

2012 | Softcover reprint of the original 1st ed. 1994
Springer-Verlag New York Inc.
978-1-4612-6931-1 (ISBN)

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This book was planned originally not as a work to be published, but as an excuse to buy a computer, incidentally to give me a chance to organize my own ideas ~n what measure theory every would-be analyst should learn, and to detail my approach to the subject. When it turned out that Springer-Verlag thought that the point of view in the book had general interest and offered to publish it, I was forced to try to write more clearly and search for errors. The search was productive. Readers will observe the stress on the following points. The application of pseudometric spaces. Pseudo metric, rather than metric spaces, are applied to obviate the artificial replacement of functions by equivalence classes, a replacement that makes the use of "almost everywhere" either improper or artificial. The words "function" and "the set on which a function has values at least E" can be taken literally in this book. Pseudometric space properties are applied in many contexts. For example, outer measures are used to pseudometrize classes of sets and the extension of a finite measure from an algebra to a 0" algebra is thereby reduced to finding the closure of a subset of a pseudo metric space.

0. Conventions and Notation.- I. Operations on Sets.- II. Classes of Subsets of a Space.- III. Set Functions.- IV. Measure Spaces.- V. Measurable Functions.- VI. Integration.- VII. Hilbert Space.- VIII. Convergence of Measure Sequences.- IX. Signed Measures.- X. Measures and Functions of Bounded Variation on R.- XI. Conditional Expectations ; Martingale Theory.- Notation.

Reihe/Serie	Graduate Texts in Mathematics ; 143
Zusatzinfo	XII, 212 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4612-6931-8 / 1461269318
ISBN-13	978-1-4612-6931-1 / 9781461269311
Zustand	Neuware