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＜電子ブック＞
Measure Theory / by J.L. Doob
(Graduate Texts in Mathematics. ISSN:21975612 ; 143)

版	1st ed. 1994.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1994
本文言語	英語
大きさ	XII, 212 p : online resource
冊子体	Measure theory / J.L. Doob ; : us,: gw
著者標目	*Doob, J.L author SpringerLink (Online service)
件　名	LCSH:Functions of real variables FREE:Real Functions
一般注記	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 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4612-0877-8

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