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The Theory of Functions of a Real Variable (Second Edition) /
This textbook leads the reader by easy stages through the essential parts of the theory of sets and theory of measure to the properties of the Lebesgue integral.
| Autor principal: | |
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| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Toronto :
University of Toronto Press,
1951.
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| Colección: | Book collections on Project MUSE.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 020 | |a 9781487599966 | ||
| 020 | |z 9781487592042 | ||
| 035 | |a (OCoLC)1389340583 | ||
| 040 | |a MdBmJHUP |c MdBmJHUP | ||
| 100 | 1 | |a Jeffery, R. L. | |
| 245 | 1 | 4 | |a The Theory of Functions of a Real Variable (Second Edition) / |c by R.L. Jeffery. |
| 264 | 1 | |a Toronto : |b University of Toronto Press, |c 1951. | |
| 264 | 3 | |a Baltimore, Md. : |b Project MUSE, |c 2023 | |
| 264 | 4 | |c ©1951. | |
| 300 | |a 1 online resource (244 pages). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 0 | |a Mathematical expositions ; |v no. 6 | |
| 505 | 0 | |a Cover -- CONTENTS -- INTRODUCTION -- 0.1. The positive integers -- 0.2. The fundamental operations on integers -- 0.3. The rational numbers -- 0.4. The irrational numbers -- 0.5. The real number system -- Problems -- I. SETS, SEQUENCES, AND FUNCTIONS -- 1.1. Bounds and limits of sets and sequences -- 1.2. Functions and their properties -- 1.3. Sequences of functions and uniform convergence -- Problems -- II. METRIC PROPERTIES OF SETS -- 2.1. Notation and definitions -- 2.2. Descriptive properties of sets -- 2.3. Metric properties of sets | |
| 505 | 0 | |a 2.4. Measurability and measurable sets2.5. Further descriptive properties of sets -- 2.6. Measure-preserving transformations and non-measurable sets -- 2.7. A non-measurable set -- Problems -- III. THE LEBESGUE INTEGRAL -- 3.1. Measurable functions -- 3.2. The Lebesgue integral -- 3.3. The Riemann integral -- 3.4. The extension of the definition of the Lebesgue integral to unbounded functions -- 3.5. Further properties of measurable functions -- Problems -- IV. PROPERTIES OF THE LEBESGUE INTEGRAL -- 4.1. Notation and conventions | |
| 505 | 0 | |a 4.2. Properties of the Lebesgue integral4.3. Definitions of summability and their extension to unbounded sets -- 4.4. The integrability of sequences -- 4.5. Integrals containing a parameter -- 4.6. Further theorems on sequences of functions -- 4.7. The ergodic theorem -- Problems -- V. METRIC DENSITY AND FUNCTIONS OF BOUNDED VARIATION -- 5.1. The Vitali covering theorem -- 5.2. Metric density of sets -- 5.3. Approximate continuity -- 5.4. Functions of bounded variation -- 5.5. Upper and lower derivatives -- 5.6. Functions of sets | |
| 505 | 0 | |a 5.7. The summability of the derivative of a function of bounded variation5.8. Functions of sets -- Problems -- VI. THE INVERSION OF DERIVATIVES -- 6.1. Functions defined by integrals, F(x) = L(f, a, x) -- 6.2. The inversion of derivatives which are not summable -- 6.3. The integrals of Denjoy and other generalized integrals -- 6.4. Descriptive definitions of generalized integrals -- Problems -- VII. DERIVED NUMBERS AND DERIVATIVES -- 7.1. Derivatives or derived numbers -- 7.2. The Weierstrass non-differentiable function | |
| 505 | 0 | |a 7.3. A function which has no unilateral derivative7.4. The derived numbers of arbitrary functions defined on arbitrary sets -- 7.5. Approximate derived numbers over arbitrary sets -- 7.6. Approximate derived numbers of measurable functions, and relations between arbitrary functions and measurable functions -- VIII. THE STIELTJES INTEGRAL -- 8.1. The Riemann-Stieltjes Integral -- 8.2. Properties of the Riemann-Stieltjes integral -- 8.3. Interval functions and measure functions -- 8.4. Linear functionals -- BIBLIOGRAPHY -- INDEX OF SUBJECTS -- A -- B -- C -- D | |
| 520 | |a This textbook leads the reader by easy stages through the essential parts of the theory of sets and theory of measure to the properties of the Lebesgue integral. | ||
| 588 | |a Description based on print version record. | ||
| 650 | 7 | |a Functions of real variables. |2 fast |0 (OCoLC)fst00936120 | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 6 | |a Fonctions de variables reelles. | |
| 650 | 0 | |a Functions of real variables. | |
| 655 | 7 | |a Electronic books. |2 local | |
| 710 | 2 | |a Project Muse. |e distributor | |
| 830 | 0 | |a Book collections on Project MUSE. | |
| 856 | 4 | 0 | |z Texto completo |u https://projectmuse.uam.elogim.com/book/107993/ |
| 945 | |a Project MUSE - Custom Collection | ||