Cargando…
The theory of functions of a real variable /
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.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Toronto :
University of Toronto Press,
1951.
|
| Colección: | Mathematical expositions ;
no. 6. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | JSTOR_ocn567918159 | ||
| 003 | OCoLC | ||
| 005 | 20231005004200.0 | ||
| 006 | m o d | ||
| 007 | cr bn||||||abp | ||
| 007 | cr bn||||||ada | ||
| 008 | 100323s1951 onc ob 001 0 eng d | ||
| 040 | |a OCLCE |b eng |e pn |c OCLCE |d OCLCQ |d OCLCF |d OCLCO |d OCLCQ |d JSTOR |d N$T |d EBLCP |d N$T |d MERUC |d YDX |d BTN |d SNK |d OCLCQ |d EZ9 |d CNLAK |d OCLCQ |d S9I |d OCLCQ |d UKAHL |d OCLCQ |d OCLCO |d OCLCQ |d P@U |d OCLCQ |d OCLCO | ||
| 019 | |a 297857000 |a 1005842873 |a 1005868230 |a 1100853194 |a 1389340583 | ||
| 020 | |a 148759996X |q (electronic bk.) | ||
| 020 | |a 9781487599966 |q (electronic bk.) | ||
| 020 | |z 9781487592042 | ||
| 029 | 1 | |a AU@ |b 000062535804 | |
| 035 | |a (OCoLC)567918159 |z (OCoLC)297857000 |z (OCoLC)1005842873 |z (OCoLC)1005868230 |z (OCoLC)1100853194 |z (OCoLC)1389340583 | ||
| 037 | |a 22573/ctt1vx0hhx |b JSTOR | ||
| 042 | |a dlr | ||
| 050 | 4 | |a QA331.5 |b .J43 | |
| 072 | 7 | |a MAT |x 005000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 034000 |2 bisacsh | |
| 082 | 0 | 4 | |a 515.8 |b J362t |
| 049 | |a UAMI | ||
| 100 | 1 | |a Jeffery, R. L. | |
| 245 | 1 | 4 | |a The theory of functions of a real variable / |c by R.L. Jeffery. |
| 260 | |a Toronto : |b University of Toronto Press, |c 1951. | ||
| 300 | |a 1 online resource (xiii, 232 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file | ||
| 490 | 1 | |a Mathematical expositions ; |v no. 6 | |
| 504 | |a Includes bibliographical references (pages 221-224). | ||
| 506 | |3 Use copy |f Restrictions unspecified |2 star |5 MiAaHDL | ||
| 533 | |a Electronic reproduction. |b [Place of publication not identified] : |c HathiTrust Digital Library, |d 2010. |5 MiAaHDL | ||
| 538 | |a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL | ||
| 583 | 1 | |a digitized |c 2010 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL | |
| 588 | 0 | |a Print version record. | |
| 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 | 8 | |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 | 8 | |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 | 8 | |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 | 8 | |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. | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 650 | 0 | |a Functions of real variables. | |
| 650 | 6 | |a Fonctions de variables réelles. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Functions of real variables |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Jeffery, R.L. |t Theory of functions of a real variable. |d Toronto : University of Toronto Press, 1951 |w (DLC) 53000755 |w (OCoLC)1201837 |
| 830 | 0 | |a Mathematical expositions ; |v no. 6. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.3138/j.ctt1vxmd19 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH35094630 | ||
| 938 | |a EBL - Ebook Library |b EBLB |n EBL5092313 | ||
| 938 | |a EBSCOhost |b EBSC |n 1613404 | ||
| 938 | |a YBP Library Services |b YANK |n 14875801 | ||
| 938 | |a Project MUSE |b MUSE |n musev2_107993 | ||
| 994 | |a 92 |b IZTAP | ||