The Resource Fundamentals of Real Analysis, by Sterling K. Berberian, (electronic resource)

Fundamentals of Real Analysis, by Sterling K. Berberian, (electronic resource)

Label
Fundamentals of Real Analysis
Title
Fundamentals of Real Analysis
Statement of responsibility
by Sterling K. Berberian
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
Integration theory and general topology form the core of this textbook for a first-year graduate course in real analysis. After the foundational material in the first chapter (construction of the reals, cardinal and ordinal numbers, Zorn's lemma and transfinite induction), measure, integral and topology are introduced and developed as recurrent themes of increasing depth. The treatment of integration theory is quite complete (including the convergence theorems, product measure, absolute continuity, the Radon-Nikodym theorem, and Lebesgue's theory of differentiation and primitive functions), while topology, predominantly metric, plays a supporting role. In the later chapters, integral and topology coalesce in topics such as function spaces, the Riesz representation theorem, existence theorems for an ordinary differential equation, and integral operators with continuous kernel function. In particular, the material on function spaces lays a firm foundation for the study of functional analysis
Member of
http://library.link/vocab/creatorName
Berberian, Sterling K
Dewey number
515
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
T0t8esRVCts
Image bit depth
0
Language note
English
LC call number
QA331.5
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Universitext,
http://library.link/vocab/subjectName
  • Mathematics
  • Real Functions
Label
Fundamentals of Real Analysis, by Sterling K. Berberian, (electronic resource)
Instantiates
Publication
Note
"With 31 figures."
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
1 Foundations -- §1.1. Logic, set notations -- §1.2. Relations -- §1.3. Functions (mappings) -- §1.4. Product sets, axiom of choice -- §1.5. Inverse functions -- §1.6. Equivalence relations, partitions, quotient sets -- §1.7. Order relations -- §1.8. Real numbers -- §1.9. Finite and infinite sets -- §1.10. Countable and uncountable sets -- §1.11. Zorn’s lemma, the well-ordering theorem -- §1.12. Cardinality -- §1.13. Cardinal arithmetic, the continuum hypothesis -- §1.14. Ordinality -- §1.15. Extended real numbers -- §1.16. limsup, liminf, convergence in ? -- 2 Lebesgue Measure -- §2.1. Lebesgue outer measure on ? -- §2.2. Measurable sets -- §2.3. Cantor set: an uncountable set of measure zero -- §2.4. Borel sets, regularity -- §2.5. A nonmeasurable set -- §2.6. Abstract measure spaces -- 3 Topology -- §3.1. Metric spaces: examples -- §3.2. Convergence, closed sets and open sets in metric spaces -- §3.3. Topological spaces -- §3.4. Continuity -- §3.5. Limit of a function -- 4 Lebesgue Integral -- §4.1. Measurable functions -- §4.2. a.e. -- §4.3. Integrable simple functions -- §4.4. Integrable functions -- §4.5. Monotone convergence theorem, Fatou’s lemma -- §4.6. Monotone classes -- §4.7. Indefinite integrals -- §4.8. Finite signed measures -- 5 Differentiation -- §5.1. Bounded variation, absolute continuity -- §5.2. Lebesgue’s representation of AC functions -- §5.3. limsup, liminf of functions; Dini derivates -- §5.4. Criteria for monotonicity -- §5.5. Semicontinuity -- §5.6. Semicontinuous approximations of integrable functions -- §5.7. F. Riesz’s “Rising sun lemma” -- §5.8. Growth estimates of a continuous increasing function -- §5.9. Indefinite integrals are a.e. primitives -- §5.10. Lebesgue’s “Fundamental theorem of calculus” -- §5.11. Measurability of derivates of a monotone function -- §5.12. Lebesgue decomposition of a function of bounded variation -- §5.13. Lebesgue’s criterion for Riemann-integrability -- 6 Function Spaces -- §6.1. Compact metric spaces -- §6.2. Uniform convergence, iterated limits theorem -- §6.3. Complete metric spaces -- §6.4. L1 -- §6.5. Real and complex measures -- §6.6. L? -- §6.7. LP(1 < p < ?) -- §6.8.C(X) -- §6.9. Stone-Weierstrass approximation theorem -- 7 Product Measure -- §7.1. Extension of measures -- §7.2. Product measures -- §7.3. Iterated integrals, Fubini—Tonelli theorem for finite measures -- §7.4. Fubini—Tonelli theorem for o--finite measures -- 8 The Differential Equation y’ =f (xy) -- §8.1. Equicontinuity, Ascoli’s theorem -- §8.2. Picard’s existence theorem for y’ =f (xy) -- §8.3. Peano’s existence theorem for y’ =f (xy) -- 9 Topics in Measure and Integration -- §9.1. Jordan-Hahn decomposition of a signed measure -- §9.2. Radon-Nikodym theorem -- §9.3. Lebesgue decomposition of measures -- §9.4. Convolution in L1(?) -- §9.5. Integral operators (with continuous kernel function) -- Index of Notations
Dimensions
unknown
Edition
1st ed. 1999.
Extent
1 online resource (XI, 479 p. 98 illus.)
File format
multiple file formats
Form of item
online
Isbn
9781461205494
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-0549-4
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089178
  • (SSID)ssj0000806387
  • (PQKBManifestationID)11498249
  • (PQKBTitleCode)TC0000806387
  • (PQKBWorkID)10748507
  • (PQKB)10572950
  • (DE-He213)978-1-4612-0549-4
  • (MiAaPQ)EBC3073921
  • (EXLCZ)993400000000089178
Label
Fundamentals of Real Analysis, by Sterling K. Berberian, (electronic resource)
Publication
Note
"With 31 figures."
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
1 Foundations -- §1.1. Logic, set notations -- §1.2. Relations -- §1.3. Functions (mappings) -- §1.4. Product sets, axiom of choice -- §1.5. Inverse functions -- §1.6. Equivalence relations, partitions, quotient sets -- §1.7. Order relations -- §1.8. Real numbers -- §1.9. Finite and infinite sets -- §1.10. Countable and uncountable sets -- §1.11. Zorn’s lemma, the well-ordering theorem -- §1.12. Cardinality -- §1.13. Cardinal arithmetic, the continuum hypothesis -- §1.14. Ordinality -- §1.15. Extended real numbers -- §1.16. limsup, liminf, convergence in ? -- 2 Lebesgue Measure -- §2.1. Lebesgue outer measure on ? -- §2.2. Measurable sets -- §2.3. Cantor set: an uncountable set of measure zero -- §2.4. Borel sets, regularity -- §2.5. A nonmeasurable set -- §2.6. Abstract measure spaces -- 3 Topology -- §3.1. Metric spaces: examples -- §3.2. Convergence, closed sets and open sets in metric spaces -- §3.3. Topological spaces -- §3.4. Continuity -- §3.5. Limit of a function -- 4 Lebesgue Integral -- §4.1. Measurable functions -- §4.2. a.e. -- §4.3. Integrable simple functions -- §4.4. Integrable functions -- §4.5. Monotone convergence theorem, Fatou’s lemma -- §4.6. Monotone classes -- §4.7. Indefinite integrals -- §4.8. Finite signed measures -- 5 Differentiation -- §5.1. Bounded variation, absolute continuity -- §5.2. Lebesgue’s representation of AC functions -- §5.3. limsup, liminf of functions; Dini derivates -- §5.4. Criteria for monotonicity -- §5.5. Semicontinuity -- §5.6. Semicontinuous approximations of integrable functions -- §5.7. F. Riesz’s “Rising sun lemma” -- §5.8. Growth estimates of a continuous increasing function -- §5.9. Indefinite integrals are a.e. primitives -- §5.10. Lebesgue’s “Fundamental theorem of calculus” -- §5.11. Measurability of derivates of a monotone function -- §5.12. Lebesgue decomposition of a function of bounded variation -- §5.13. Lebesgue’s criterion for Riemann-integrability -- 6 Function Spaces -- §6.1. Compact metric spaces -- §6.2. Uniform convergence, iterated limits theorem -- §6.3. Complete metric spaces -- §6.4. L1 -- §6.5. Real and complex measures -- §6.6. L? -- §6.7. LP(1 < p < ?) -- §6.8.C(X) -- §6.9. Stone-Weierstrass approximation theorem -- 7 Product Measure -- §7.1. Extension of measures -- §7.2. Product measures -- §7.3. Iterated integrals, Fubini—Tonelli theorem for finite measures -- §7.4. Fubini—Tonelli theorem for o--finite measures -- 8 The Differential Equation y’ =f (xy) -- §8.1. Equicontinuity, Ascoli’s theorem -- §8.2. Picard’s existence theorem for y’ =f (xy) -- §8.3. Peano’s existence theorem for y’ =f (xy) -- 9 Topics in Measure and Integration -- §9.1. Jordan-Hahn decomposition of a signed measure -- §9.2. Radon-Nikodym theorem -- §9.3. Lebesgue decomposition of measures -- §9.4. Convolution in L1(?) -- §9.5. Integral operators (with continuous kernel function) -- Index of Notations
Dimensions
unknown
Edition
1st ed. 1999.
Extent
1 online resource (XI, 479 p. 98 illus.)
File format
multiple file formats
Form of item
online
Isbn
9781461205494
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-0549-4
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089178
  • (SSID)ssj0000806387
  • (PQKBManifestationID)11498249
  • (PQKBTitleCode)TC0000806387
  • (PQKBWorkID)10748507
  • (PQKB)10572950
  • (DE-He213)978-1-4612-0549-4
  • (MiAaPQ)EBC3073921
  • (EXLCZ)993400000000089178

Library Locations

  • Architecture LibraryBorrow it
    Gould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US
    35.205706 -97.445050
  • Bizzell Memorial LibraryBorrow it
    401 W. Brooks St., Norman, OK, 73019, US
    35.207487 -97.447906
  • Boorstin CollectionBorrow it
    401 W. Brooks St., Norman, OK, 73019, US
    35.207487 -97.447906
  • Chinese Literature Translation ArchiveBorrow it
    401 W. Brooks St., RM 414, Norman, OK, 73019, US
    35.207487 -97.447906
  • Engineering LibraryBorrow it
    Felgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US
    35.205706 -97.445050
  • Fine Arts LibraryBorrow it
    Catlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US
    35.210371 -97.448244
  • Harry W. Bass Business History CollectionBorrow it
    401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • History of Science CollectionsBorrow it
    401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • John and Mary Nichols Rare Books and Special CollectionsBorrow it
    401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • Library Service CenterBorrow it
    2601 Technology Place, Norman, OK, 73019, US
    35.185561 -97.398361
  • Price College Digital LibraryBorrow it
    Adams Hall 102 307 West Brooks St., Norman, OK, 73019, US
    35.210371 -97.448244
  • Western History CollectionsBorrow it
    Monnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US
    35.209584 -97.445414
Processing Feedback ...