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 StorageQA331.5 .R6 1988 Browse related items Request

    Details

    Subject(s)
    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.
    ISBN
    • 0024041513
    • 9780024041517
    • 0029466202 ((International ed.))
    • 9780029466209 ((International ed.))
    LCCN
    86033216
    OCLC
    15055353
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