Atjaunināt sīkdatņu piekrišanu

E-grāmata: Modern Real Analysis

Contributions by ,
  • Formāts: EPUB+DRM
  • Sērija : Graduate Texts in Mathematics 278
  • Izdošanas datums: 30-Nov-2017
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319646299
Citas grāmatas par šo tēmu:
  • Formāts - EPUB+DRM
  • Cena: 64,23 €*
  • * ši ir gala cena, t.i., netiek piemērotas nekādas papildus atlaides
  • Ielikt grozā
  • Pievienot vēlmju sarakstam
  • Šī e-grāmata paredzēta tikai personīgai lietošanai. E-grāmatas nav iespējams atgriezt un nauda par iegādātajām e-grāmatām netiek atmaksāta.
Modern Real AnalysisPalielināt
  • Formāts: EPUB+DRM
  • Sērija : Graduate Texts in Mathematics 278
  • Izdošanas datums: 30-Nov-2017
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319646299
Citas grāmatas par šo tēmu:

DRM restrictions

  • Kopēšana (kopēt/ievietot):

    nav atļauts

  • Drukāšana:

    nav atļauts

  • Lietošana:

    Digitālo tiesību pārvaldība (Digital Rights Management (DRM))
    Izdevējs ir piegādājis šo grāmatu šifrētā veidā, kas nozīmē, ka jums ir jāinstalē bezmaksas programmatūra, lai to atbloķētu un lasītu. Lai lasītu šo e-grāmatu, jums ir jāizveido Adobe ID. Vairāk informācijas šeit. E-grāmatu var lasīt un lejupielādēt līdz 6 ierīcēm (vienam lietotājam ar vienu un to pašu Adobe ID).

    Nepieciešamā programmatūra
    Lai lasītu šo e-grāmatu mobilajā ierīcē (tālrunī vai planšetdatorā), jums būs jāinstalē šī bezmaksas lietotne: PocketBook Reader (iOS / Android)

    Lai lejupielādētu un lasītu šo e-grāmatu datorā vai Mac datorā, jums ir nepieciešamid Adobe Digital Editions (šī ir bezmaksas lietotne, kas īpaši izstrādāta e-grāmatām. Tā nav tas pats, kas Adobe Reader, kas, iespējams, jau ir jūsu datorā.)

    Jūs nevarat lasīt šo e-grāmatu, izmantojot Amazon Kindle.

This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a definitive and self-contained manner, it features a natural progression of concepts from simple to difficult. Several innovative topics are featured, including differentiation of measures, elements of Functional Analysis, the Riesz Representation Theorem, Schwartz distributions, the area formula, Sobolev functions and applications to harmonic functions. Together, the selection of topics forms a sound foundation in real analysis that is particularly suited to students going on to further study in partial differential equations.

This second edition of Modern Real Analysis contains many substantial improvements, including the addition of problems for practicing techniques, and an entirely new section devoted to the relationship between Lebesgue and improper integrals. Aimed at graduate students with an understanding of advanced calculus, the text will also appeal to more experienced mathematicians as a useful reference.

Recenzijas

This book provides an accessible self-contained introduction to modern real analysis suitable for graduate students with an understanding of advanced calculus. It may also provide a useful reference for more experienced mathematicians. The focus of the book is on measure and integration, which are nicely connected to closely related topics such as bounded variations and absolutely continuous functions representations theorems for linear functionals, Sovolev spaces and distribution. (Gareth Speight, Mathematical Reviews, October, 2018)

1 Preliminaries
1(10)
1.1 Sets
1(2)
1.2 Functions
3(3)
1.3 Set Theory
6(5)
2 Real, Cardinal, and Ordinal Numbers
11(22)
2.1 The Real Numbers
11(10)
2.2 Cardinal Numbers
21(7)
2.3 Ordinal Numbers
28(5)
3 Elements of Topology
33(36)
3.1 Topological Spaces
33(5)
3.2 Bases for a Topology
38(2)
3.3 Metric Spaces
40(5)
3.4 Meager Sets in Topology
45(3)
3.5 Compactness in Metric Spaces
48(3)
3.6 Compactness of Product Spaces
51(2)
3.7 The Space of Continuous Functions
53(10)
3.8 Lower Semicontinuous Functions
63(6)
4 Measure Theory
69(50)
4.1 Outer Measure
69(9)
4.2 Caratheodory Outer Measure
78(3)
4.3 Lebesgue Measure
81(6)
4.4 The Cantor Set
87(2)
4.5 Existence of Nonmeasurable Sets
89(2)
4.6 Lebesgue-Stieltjes Measure
91(4)
4.7 Hausdorff Measure
95(6)
4.8 Hausdorff Dimension of Cantor Sets
101(2)
4.9 Measures on Abstract Spaces
103(6)
4.10 Regular Outer Measures
109(5)
4.11 Outer Measures Generated by Measures
114(5)
5 Measurable Functions
119(22)
5.1 Elementary Properties of Measurable Functions
119(11)
5.2 Limits of Measurable Functions
130(5)
5.3 Approximation of Measurable Functions
135(6)
6 Integration
141(68)
6.1 Definitions and Elementary Properties
141(6)
6.2 Limit Theorems
147(4)
6.3 Riemann and Lebesgue Integration: A Comparison
151(4)
6.4 Improper Integrals
155(2)
6.5 Lp Spaces
157(10)
6.6 Signed Measures
167(6)
6.7 The Radon--Nikodym Theorem
173(7)
6.8 The Dual of Lp
180(6)
6.9 Product Measures and Fubini's Theorem
186(10)
6.10 Lebesgue Measure as a Product Measure
196(1)
6.11 Convolution
197(4)
6.12 Distribution Functions
201(1)
6.13 The Marcinkiewicz Interpolation Theorem
202(7)
7 Differentiation
209(50)
7.1 Covering Theorems
209(5)
7.2 Lebesgue Points
214(5)
7.3 The Radon--Nikodym Derivative: Another View
219(6)
7.4 Functions of Bounded Variation
225(5)
7.5 The Fundamental Theorem of Calculus
230(6)
7.6 Variation of Continuous Functions
236(5)
7.7 Curve Length
241(7)
7.8 The Critical Set of a Function
248(5)
7.9 Approximate Continuity
253(6)
8 Elements of Functional Analysis
259(42)
8.1 Normed Linear Spaces
259(8)
8.2 Hahn-Banach Theorem
267(3)
8.3 Continuous Linear Mappings
270(5)
8.4 Dual Spaces
275(10)
8.5 Hilbert Spaces
285(10)
8.6 Weak and Strong Convergence in Lp
295(6)
9 Measures and Linear Functionals
301(16)
9.1 The Daniell Integral
301(8)
9.2 The Riesz Representation Theorem
309(8)
10 Distributions
317(18)
10.1 The Space D
317(5)
10.2 Basic Properties of Distributions
322(3)
10.3 Differentiation of Distributions
325(5)
10.4 Essential Variation
330(5)
11 Functions of Several Variables
335(40)
11.1 Differentiability
335(6)
11.2 Change of Variables
341(11)
11.3 Sobolev Functions
352(7)
11.4 Approximating Sobolev Functions
359(4)
11.5 Sobolev Embedding Theorem
363(4)
11.6 Applications
367(2)
11.7 Regularity of Weakly Harmonic Functions
369(6)
Bibliography 375(4)
Index 379
William P. Ziemer is Professor Emeritus of Mathematics at Indiana University, and is the author of the highly influential GTM (vol. 120), Weakly Differentiable Functions.





Monica Torres is Associate Professor of Mathematics at Purdue University, specializing in geometric measure theory and partial differential equations.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
Permanent link: https://www.kriso.lv/db/97833196462996e.html
Keywords: