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Theory of Measures and Integration

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ISBN-10: 0471249777

ISBN-13: 9780471249771

Edition: 2003

Authors: Eric M. Vestrup

List price: $171.00
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Mirroring the natural progression of topics found in higher-level college and graduate courses in the theory of probability, 'Measure Theory and Its Applications' offers a comprehensive collection of measure theory with emphasis on Lebesgue measure and integration of Euclidean space.
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Book details

List price: $171.00
Copyright year: 2003
Publisher: John Wiley & Sons, Incorporated
Publication date: 9/18/2003
Binding: Hardcover
Pages: 624
Size: 9.75" wide x 6.25" long x 1.50" tall
Weight: 2.134
Language: English

Set Systems
[pi]-Systems, [lambda]-Systems, and Semirings
The Borel [sigma]-Field
The k-Dimensional Borel [sigma]-Field
[sigma]-Fields: Construction and Cardinality
A Class of Ethereal Borel Sets
Continuity of Measures
A Class of Measures
Appendix: Proof of the Stieltjes Theorem
Extensions of Measures
Extensions and Restrictions
Outer Measures
Caratheodory's Criterion
Existence of Extensions
Uniqueness of Measures and Extensions
The Completion Theorem
The Relationship Between [sigma](A) and M([mu]*)
A Further Description of M([mu]*)
A Correspondence Theorem
Lebesgue Measure
Lebesgue Measure: Existence and Uniqueness
Lebesgue Sets
Translation Invariance of Lebesgue Measure
Linear Transformations
The Existence of non-Lebesgue Sets
The Cantor Set and the Lebesgue Function
A Non-Borel Lebesgue Set
The Impossibility Theorem
Excursus: "Extremely Nonmeasurable Sets"
Measurable Functions
Combining Measurable Functions
Sequences of Measurable Functions
Almost Everywhere
Simple Functions
Some Convergence Concepts
Continuity and Measurability
A Generalized Definition of Measurability
The Lebesgue Integral
Stage One: Simple Functions
Stage Two: Nonnegative Functions
Stage Three: General Measurable Functions
Stage Four: Almost Everywhere Defined Functions
Integrals Relative to Lebesgue Measure
Step Functions in Euclidean Space
The Riemann Integral, Part One
The Riemann Integral, Part Two
Change of Variables in the Linear Case
The L[superscript p] Spaces
L[superscript p] Space: The Case 1 [less than or equal] p [less than sign] +[infinity]
The Riesz--Fischer Theorem
L[superscript p] Space: The Case 0 [less than sign] p [less than sign] 1
L[superscript p] Space: The Case p = +[infinity]
Containment Relations For L[superscript p] Spaces
More Convergence Concepts
Prelude to the Riesz Representation Theorem
The Riesz Representation Theorem
The Radon-Nikodym Theorem
The Radon-Nikodym Theorem, Part I
The Radon-Nikodym Theorem, Part II
From Radon-Nikodym to Riesz Representation
Martingale Theorems
Products of Two Measure Spaces
Product Measures
The Fubini Theorems
The Fubini Theorems in Euclidean Space
The Generalized Minkowski Inequality
The Hard y-Littlewood Theorems
Arbitrary Products of Measure Spaces
Notation and Conventions
Construction of the Product Measure
Convergence Theorems in Product Space
The L[superscript 2] Strong Law
Prelude to the L[superscript 1] Strong Law
The L[superscript 1] Strong Law