The Kurzweil-Henstock integral and its differential : a unified theory of integration on R and RN /
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton, FL :
CRC Press, an imprint of Taylor and Francis,
2001.
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| Edition: | First edition. |
| Series: | Chapman & Hall/CRC research notes in mathematics series.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Chapter0.1 The Gauge-Directed Integral
- chapter0.2 Differentials
- chapter0.3 Guidance for the Reader
- chapter 1 Integration of Summants1.1 Cells, Figures and Partitions
- chapter1.2 Tagged Cells, Divisions, and Gauges
- chapter over a Figure
- chapter1.4 Summants with Special Properties
- chapter Boolean Algebra of Figures
- chapter1.6 Uniform Integrability and Its Consequences
- chapter1.7 Term-by-Term Integration of Series
- chapter tion
- chapter1.9 Integration over Arbitrary Intervals
- chapter2.1 Differential Equivalence and Differentials
- chapter on K
- chapter2.3 Differential Norm and Summable Differentials
- chapter ferentials
- chapter2.5 The Differential dg of a Function g
- chapter2.6 The Total Variation of a Function on a Cell K
- chapter2.7 Functions as Differential Coefficients
- chapter orems
- chapter Differentials
- chapter3.2 Continuous Differentials
- chapter3.3 Archimedean Properties for Differentials
- chapter3.4 Differentials on Open-Ended Intervals
- chapter3.5-Nullity of the Union of All-Null Cells
- chapter Functions
- chapter3.7 n-Differentials on a Cell K
- chapter 4 Measurable Sets and Functions4.1 Measurable Sets
- chapter4.2 The Hahn Decomposition for Differentials
- chapter4.3 Measurable Functions
- chapter4.4 Step Functions and Regulated Functions
- chapter4.5 The Radon-Nikodym Theorem for Differentials
- chapter4.6 Minimal Measurable Dominators
- chapter5.1 The Vitali Covering Theorem with some Applications to Upper Integrals
- chapter5.3 Continuity-Everywhere of p Given 0
- chapter 6 Derivatives and Differentials6.1 Differential Coefficients from the Gradient
- chapter6.2 Integration by Parts and Taylor's Formula
- chapter culus
- chapter Using Essential Limits
- chapter6.5 Differentiation Under the Integral Sign
- chapter 7 Essential Properties of Functions7.1 Essentially Bounded Functions
- chapter7.2 Essentially Regulated Functions
- chapter7.3 Essential Variation
- chapter Differentials
- chapter Differentials
- chapter8.3 Absolutely Continuous Functions
- chapter8.4 The Vitali Convergence Theorem
- chapter9.1 Banach's Indicatrix Theorem
- chapter Applications
- chapter10.1 Integral and Differential on n-Cells
- chapter10.2 Direct Products of Summants
- chapter10.4 Integration on Paths in Rn
- chapter10.5 Green's Theorem
- chapter 11 Mathematical Background11.1 Filterbases, Lower and Upper Limits.