Aspects of integration : novel approaches to the Riemann and Lebesgue integrals /: novel approaches to the Riemann and Lebesgue integrals. (2023)

• Record Type: Book
• Further Information: Note: Ronald B. Guenther, John W. Lee.
• Authors: Guenther, Ronald B; Lee, John W, 1942-
• Contents: I. A Novel Approach to Riemann Integration. 1. Preliminaries. 1.1. Sums of Powers of Positive Integers. 1.2. Bernstein Polynomials. 2. The Riemann Integral. 2.1. Method of Exhaustion. 2.2. Integral of a Continuous Function. 2.3. Foundational Theorems of Integral Calculus. 2.4. Integration by Substitution. 3. Extension to Higher Dimensions. 3.1. Method of Exhaustion. 3.2. Bernstein Polynomials in 2 Dimensions. 3.3. Integral of a Continuous Function. 4. Extension to the Lebesgue Integral. 4.1. Convergence and Cauchy Sequences. 4.2. Completion of the Rational Numbers. 4.3. Completion of C in the 1-norm. II. Lebesgue Integration. 5. Riesz-Nagy Approach. 5.1. Null Sets and Sets of Measure Zero. 5.2. Lemmas A and B. 5.3. The Class C1. 5.4. The Class C2. 5.5. Convergence Theorems. 5.6. Completeness. 5.7. The C2-Integral is the Lebesgue Integral. 6. Comparing Integrals. 6.1. Properly Integrable Functions. 6.2. Characterization of the Riemann Integral. 6.3. Riemann vs. Lebesgue Integrals. 6.4. The Novel Approach. A. Dinis Lemma. B. Semicontinuity. C. Completion of a Normed Linear Space. Bibliography. Index.
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2023
• Extent: 1 online resource (160 pages)
• Subjects: 515.43; Riemann integral; Lebesgue integral
• Languages: English
• ISBNs: 9781000925944; 9781000925937
• Related ISBNs: 9781032481128
• Notes: Note: Description based on CIP data; resource not viewed.
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