Kemaren, aku sedang Chatting dengan teman yang sedang melanjutkan kuliah di Institut Pertanian Bogor (IPB). Dia sedang Studi S2 PRogram studi Matematika Terapan. Dia mengatakan bahwa untuk kuliah analisis realnya menggunakan buku karangan H.R. Royden. Katanya nyari bukunya susah. KEbetulan aku punya, jadi aku bagi deh. heheheheh🙂

Buat teman-teman laen yang pengen belajar analisis real karangan H.R Royden ini, Silahkan download saja di link berikut ini…..

Sinopsis Buku Real Analysis Karangan H.R. Royden edisi ke-4 yaitu :

Real Analysis (4th Edition)
By Halsey Royden, Patrick Fitzpatrick

  • Publisher: Prentice Hall
  • Number Of Pages: 544
  • Publication Date: 2010-01-15
  • ISBN-10 / ASIN: 013143747X
  • ISBN-13 / EAN: 9780131437470
Analisis Real, Edisi Keempat, meliputi materi dasar yang setiap pembaca harus tahu dalam teori klasik fungsi ukuran, variabel real dan teori integrasi, dan beberapa topik yang lebih penting dan dasar dalam umum topologi dan teoriruang bernorma linier. Teks ini mengasumsikan latar belakang umum dalam matematika dan keakraban dengan konsep-konsep dasar analisis.Klasik teori fungsi, termasuk ruang Banach klasik; topologi Umum dan teori ruang Banach umum, pengobatan Abstrak ukuran dan integrasi.Untuk semua pembaca tertarik pada analisis real. Berikut daftar isi yang disajikan dalam buku ini :

Daftar Isi
Preface
Contents
PART ONE: LEBESGUE INTEGRATION FOR FUNCTIONS OF ASINGLE REALVARIABLE
  • Preliminaries on Sets, Mappings, and Relations
    • UNIONS AND INTERSECTIONS OF SETS
    • EQUIVALENCE RELATIONS, THE AXIOM OF CHOICE, AND ZORN’S LEMMA
  • 1 The Real Numbers: Sets,Sequences, and Functions
    • 1.1 THE FIELD, POSITIVITY, AND COMPLETENESS AXIOMS
    • 1.2 THE NATURAL AND RATIONAL NUMBERS
    • 1.3 COUNTABLE AND UNCOUNTABLE SETS
    • 1.4 OPEN SETS, CLOSED SETS, AND BOREL SETS OF REAL NUMBERS
    • 1.5 SEQUENCES OF REAL NUMBERS
    • 1.6 CONTINUOUS REAL-VALUED FUNCTIONS OF A REAL VARIABLE
  • 2 Lebesgue Measure
    • 2.1 INTRODUCTION
    • 2.2 LEBESGUE OUTER MEASURE
    • 2.3 THE u-ALGEBRA OF,LEBESGUE MEASURABLE SETS
    • 2.4 OUTER AND INNER APPROXIMATION OF LEBESGUE MEASURABLE SETS
    • 2.5 COUNTABLE ADDmvITY, CONTINUITY, AND THE BOREL-CANTELLI LEMMA
    • 2.6 NONMEASURABLE SETS
    • 2.7 THE CANTOR SET AND THE CANTOR-LEBESGUE FUNCTION
  • 3 Lebesgue Measurable Functions
    • 3.1 SUMS, PRODUCTS, AND COMPOSITIONS
    • 3.2 SEQUENTIAL POINTWISE UMITS AND SIMPLE APPROXIMATION
    • 3.3 LmLEWOOD’S THREE PRINCIPLES, EGOROFF’S THEOREM, AND LUSIN’S THEOREM
  • 4 Lebesgue Integration
    • 4.1 THE RIEMANN INTEGRAL
    • 4.2 THE LEBESGUE INTEGRAL OF A BOUNDED MEASURABLE FUNCTION OVER A SET OF FINITE MEASURE
    • 4.3 THE LEBESGUE INTEGRAL OF A MEASURABLE NONNEGATIVE FUNCTION
    • 4.4 THE GENERAL LEBESGUE INTEGRAL
    • 4.5 COUNTABLE ADDITIVITY AND CONTINUITY OF INTEGRATION
    • 4.6 UNIFORM INTEGRABILITY: THE VrrALI CONVERGENCE THEOREM
  • 5 Lebesgue Integration: Further Topics
    • 5.1 UNIFORM INTEGRABILITY AND TIGHTNESS: A GENERAL VITALI CONVERGENCE THEOREM
    • 5.2 CONVERGENCE IN MEASURE
    • 5.3 CHARACTERIZATIONS OF RIEMANN AND LEBESGUE INTEGRABILITY
  • 6 Differentiation and Integration
    • 6.1 CONTINUITY OF MONOTONE FUNCTIONS
    • 6.2 DIFFERENTIABILITY OF MONOTONE FUNCTIONS: LEBESGUE’S THEOREM
    • 6.3 FUNCTIONS OF BOUNDED VARIATION: JORDAN’S THEOREM
    • 6.4 ABSOLUTELY CONTINUOUS FUNCTIONS
    • 6.5 INTEGRATING DERIVATIVES: DIFFERENTIATING INDEFINITE INTEGRALS
    • 6.6 CONVEX FUNCTIONS
  • 7 The L^p Spaces: Completenessand Approximation
    • 7.1 NORMED UNEAR SPACES
    • 7.2 THE INEQUALITIES OF YOUNG, HOLDER, AND MINKOWSKI
    • 7.3 L^p COMPLETE: THE RIESZ-FISCHER THEOREM
    • 7.4 APPROXIMATION AND SEPARABILITY
  • 8 The L^p Spaces: Duality and Weak Convergence
    • 8.1 THE RIESZ REPRESENTATION FOR THE DUAL OF L^p
    • 8.2 WEAK SEQUENTIAL CONVERGENCE IN L^p
    • 8.3 WEAK SEQUENTIAL COMPACTNESS
    • 8.4 THE MINIMIZATION OF CONVEX FUNCTIONALS
PART TWO: ABSTRACT SPACES: METRIC,TOPOLOGICAL, BANACH, AND HILBERT SPACES
  • 9 Metric Spaces: General Properties
    • 9.1 EXAMPLES OF METRIC SPACES
    • 9.2 OPEN SETS, CLOSED SETS, AND CONVERGENT SEQUENCES
    • 9.3 CONTINUOUS MAPPINGS BETWEEN METRIC SPACES
    • 9.4 COMPLETE METRIC SPACES
    • 9.5 COMPACT METRIC SPACES
    • 9.6 SEPARABLE METRIC SPACES
  • 10 Metric Spaces: Three Fundamental Theorems
    • 10.1 THE ARZELA-ASCOLI THEOREM
    • 10.2 THE BAIRE CATEGORY THEOREM
    • 10.3 THE BANACH CONTRACTION PRINCIPLE
  • 11 Topological Spaces: General Properties
    • 11.1 OPEN SETS, CLOSED SETS, BASES, AND SUBBASES
    • 11.2 THE SEPARATION PROPERTIES
    • 11.3 COUNTABILITY AND SEPARABILITY
    • 11.4 CONTINUOUS MAPPINGS BETWEEN TOPOLOGICAL SPACES
    • 11.5 COMPACT TOPOLOGICAL SPACES
    • 11.6 CONNECTED TOPOLOGICAL SPACES
  • 12 Topological Spaces: Three Fundamental Theorems
    • 12.1 URYSOHN’S LEMMA AND THE TIETZE EXTENSION THEOREM
    • 12.2 THE TYCHONOFF PRODUCT THEOREM
    • 12.3 THE STONE-WEIERSTRASS THEOREM
  • 13 Continuous Linear Operators Between Banach Spaces
    • 13.1 NORM ED LINEAR SPACES
    • 13.2 LINEAR OPERATORS
    • 13.3 COMPACTNESS LOST: INFINITE [)fIlt1ENSIONAL NORM ED LINEAR SPACES
    • 13.4 THE OPEN MAPPING AND CLOSED GRAPH THEOREMS
    • 13.5 THE UNIFORM BOUNDEDNESS PRINCIPLE
  • 14 Duality for Normed Linear Spaces
    • 14.1 LINEAR FUNCTIONALS, BOUNDED LINEAR FUNCTIONALS, AND WEAK TOPOLOGIES
    • 14.2 THE HAHN-BANACH THEOREM
    • 14.3 REFLEXIVE BANACH SPACES AND WEAK SEQUENTIAL CONVERGENCE
    • 14.4 LOCALLY CONVEX TOPOLOGICAL VECTOR SPACES
    • 14.5 THE SEPARATION OF CONVEX SETS AND MAZUR’S THEOREM
    • 14.6 THE KREIN-MILMAN THEOREM
  • 15 Compactness Regained: The Weak Topology
    • 15.1 ALAOGLU’S EXTENSION OF HELLEY’S THEOREM
    • 15.2 REFLEXIVITY AND WEAK COMPACTNESS: KAKUTANI’S THEOREM
    • 15.3 COMPACTNESS AND WEAK SEQUENTIAL COMPACTNESS: THE EBERLEIN-SMULIAN THEOREM
    • 15.4 METRIZABILITY OF WEAK TOPOLOGIES
  • 16 Continuous Linear Operators on Hilbert Spaces
    • 16.1 THE INNER PRODUCT AND ORTHOGONALITY
    • 16.2 THE DUAL SPACE AND WEAK SEQUENTIAL CONVERGENCE
    • 16.3 BESSEL’S INEQUALITY AND ORTHONORMAL BASES
    • 16.4 ADJOINTS AND SYMMETRY FOR LINEAR OPERATORS
    • 16.5 COMPACT OPERATORS
    • 16.6 THE HILBERT-SCHMIDT THEOREM
    • 16.7 THE RIESZ-SCHAUDER THEOREM: CHARACTERIZATION OF FREDHOLM OPERATORS
PART THREE: MEASURE AND INTEGRATION: GENERAL THEORY
  • 17 General Measure Spaces: Their Properties and Construction
    • 17.1 MEASURES AND MEASURABLE SETS
    • 17.2 SIGNED MEASURES: THE HAHN AND JORDAN DECOMPOSITIONS
    • 17.3 THE CARATHEODORY MEASURE INDUCED BY AN OUTER MEASURE
    • 17.5 THE CARATHEODORY-HAHN THEOREM: THE EXTENSION OF A PREMEASURETO A MEASURE
  • 18 Integration Over General Measure Spaces
    • 18.1 MEASURABLE FUNCTIONS
    • 18.2 INTEGRATION OF NONNEGATIVE MEASURABLE FUNCTIONS
    • 18.3 INTEGRATION OF GENERAL MEASURABLE FUNCTIONS
    • 18.4 THE RADON-NIKODYM THEOREM
    • 18.5 THE NIKODYM METRIC SPACE: THE VITAU-HAHN-SAKS THEOREM
  • 19 General L^p Spaces: Completeness, Duality, and Weak Convergence
    • 19.1 THE COMPLETENESS OF L^p(X,u)
    • 19.2 THE RIESZ REPRESENTATION THEOREM FOR THE DUAL OF L^p
    • 19.3 THE KANTOROVITCH REPRESENTATION THEOREM FOR THE DUAL OF L^oo
    • 19.4 WEAK SEQUENTIAL COMPACTNESS IN LP{X,u)
    • 19.5 WEAK SEQUENTIAL COMPACTNESS IN L^1(X,u): THE DUNFORD-PETTIS THEOREM
  • 20 The Construction of Particular Measures
    • 20.1 PRODUCT MEASURES: THE THEOREMS OF FUBINI AND TONELLI
    • 20.2 LEBESGUE MEASURE ON EUCLIDEAN SPACE R^n
    • 20.3 CUMULATIVE DISTRIBUTION FUNCTIONS AND BOREL MEASURES ON R
    • 20.4 CARATHEODORY OUTER MEASURES AND HAUSDORFF MEASURES ON A METRIC SPACE
  • 21 Measure and Topology
    • 21.1 LOCALLY COMPACT TOPOLOGICAL SPACES
    • 21.2 SEPARATING SETS AND EXTENDING FUNCTIONS
    • 21.3 THE CONSTRUCTION OF RADON MEASURES
    • 21.4 THE REPRESENTATION OF POSITIVE LINEAR FUNCTIONALS ON Cc(X): THE RIESZ-MARKOV THEOREM
    • 21.5 THE RIESZ REPRESENTATION THEOREM FOR THE DUAL OF C(X)
    • 21.6 REGULARITY PROPERTIES OF BAIRE MEASURES
  • 22 Invariant Measures
    • 22.1 TOPOLOGICAL GROUPS: THE GENERAL LINEAR GROUP
    • 22.2 KAKUTANI’S FIXED POINT THEOREM
    • 22.3 INVARIANT BOREL MEASURES ON COMPACT GROUPS: VON NEUMANN’S THEOREM
    • 22.4 MEASURE PRESERVING TRANSFORMATIONS AND ERGODICITY: THE BOGOLIUBOV-KRILOV THEOREM
Wow,, Sangat berbeda dengan buku Introduction To real Analysis karangan Robert Bartle dan Donal Sherbert yang hanya pengantar saja. Tapi untuk yang ini adalah analisis real tingkat lanjut yah….. hehehehe…
Bagi teman-teman sekalian yang mau mendownload bukunya,, silahkan klik di sini….. paswordnya ebooksclub.org
Gratis kok….. Gak pake bayar. Hanya untuk orang indonesia yang maunya gratis-gratis ajah… hehehehehe…