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Princeton University Library Catalog
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Real analysis / H.L. Royden.
Author
Royden, H. L., 1928-1993
[Browse]
Format
Book
Language
English
Εdition
3rd ed.
Published/Created
New York : Macmillan ; London : Collier Macmillan, ©1988.
Description
xvii, 444 pages ; 25 cm
Availability
Copies in the Library
Location
Call Number
Status
Location Service
Notes
ReCAP - Remote Storage
QA331.5 .R6 1988
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Details
Subject(s)
Functions of real variables
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Functional analysis
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Measure theory
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Notes
Includes indexes.
Bibliographic references
Bibliography: p. 435-436.
Contents
1. Set theory. Functions
Unions, intersections, and complements
Algerbras of sets
The axiom of choice and infinite direct products
Countable sets
Relations and equivalences
Partial orderings and the maximal principle
Well ordering and the countable ordinals. I. Theory of functions of a real variable. 2. The real number system. Axionms for the real numbers
The natural and rational numbers as subsets of R
The extended real numbers
Sequences of real numbers
Open and closed sets of real numbers
Continuous functions
Borel sets. 3. Lebesgue measure. Outer measure
Measurable sets and Lebesgue measure
A nonmeasurable set
Measurable functions
Littlewood's three principles. 4. The Lebesgue integral. The Riemann integral
The Lebesgue integral of a bounded function over a set of finite measure
The integral of a nonnegative function
The general Lebesgue integral.
Convergence in measure. 5. Differentiation and integration. Functions of bounded variation
Differentiation of an integral
Absolute continuity
Convex functions. 6. The classical banach spaces. The Lp spaces
The Minkowski and Holder inequalities
Convergence and completeness
Approximation in L
Bounded linear functionals on the L spaces. II. Abstract spaces. 7. Metric spaces. Open and closed sets
Continuous functionals and homeomorphisms
Uniform continuity and uniformity
Subspaces
Compact metric spaces
Baire category
Absoulte G's
The Ascoli-Arzela theorem. 8. topological spaces. Fundamental notions
Bases and countability
The separation axioms and continuous real-valued functions
connectedness
Products and direct unions of topological spaces
Topological and uniform properties
Nets.
9. Compact and locally compact spaces. Compact spaces
countable compactness and the Bolzano-Weierstrass property
Products of compact spaces
Locally compact spaces
O-compact spaces
Paracompact spaces
Manifolds
The Stone-Cech compactification
The Stone-Weierstrass theorem. 10. Banach spaces. Linear operators
Linear functionals and the Hahn-Banach theorem
The closed graph theorem
Topological vector spaces
Weak topologies
Convexity
Hilbert space. III. General measure and integration theory. Measure and integration. Measure spaces
Integration
General convergence theorems
Signed measures
The Radon-Nikodym theorem
The L-spaces. 12. Measure and outer measure. Outer measure and measurability
The extension theorem
The Lebesgure-Stieltjes integral
Product measures
Integral operators
Inner measure.
Extension by sets of measure zero
Caratheodory outer measure
Hausdorff measure. 13. Measure and topology. Baire sets and Borel sets
The regularity of the Baire and Borel measures
Bounded linear functionals on C(X). 14. Invariant measures. Homogeneous spaces
Topological equicontinuity
The existence of invarient measures
Topological groups
Group actions and quotient spaces
Unicity of invariant measures
Groups of diffeomorphisms. 15. Mappings of measure spaces. Point mappings and set mappings
Boolean Ơ-algerbras
Measure algerbras
Borel equivalences
Borel measures on complete separable metric spaces
Set mappings and point mappings on complete separable metric spaces
The isometries of L. 16. The Daniell integral. The extension theorem
Uniqueness
Measureability and measure.
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ISBN
0024041513
9780024041517
0029466202 ((International ed.))
9780029466209 ((International ed.))
LCCN
86033216
OCLC
15055353
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Real analysis / H.L. Royden.
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