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1.

図書

図書
Elliot Mendelson
出版情報: New York : Academic Press, c1973  xii, 358 p. ; 24 cm
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2.

図書

図書
Avner Friedman
出版情報: New York : Holt, Rinehart and Winston, [1970]  vi, 250 p. ; 24 cm
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3.

図書

図書
J. Dieudonné
出版情報: New York : Academic Press, 1960  xiv, 361 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; v. 10
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4.

図書

図書
[by] Douglas A. Clarke [and others]
出版情報: New York : Appleton-Century-Crofts, [1971]  xiii, 363 p ; 25 cm
シリーズ名: The Appleton-Century mathematics series
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5.

図書

図書
Richard Johnsonbaugh, W. E. Pfaffenberger
出版情報: New York, N.Y. : M. Dekker, c1981  viii, 428 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 62
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目次情報: 続きを見る
Preface
Preface to the Dover Edition
Sets and Functions / I:
Sets / 1.:
Functions / 2.:
The Real Number System / II:
The Algebraic Axioms of the Real Numbers / 3.:
The Order Axiom of the Real Numbers / 4.:
The Least-Upper-Bound Axiom / 5.:
The Set of Positive Integers / 6.:
Integers, Rationals, and Exponents / 7.:
Set Equivalence / III:
Definitions and Examples / 8.:
Countable and Uncountable Sets / 9.:
Sequences of Real Numbers / IV:
Limit of a Sequence / 10.:
Subsequences / 11.:
The Algebra of Limits / 12.:
Bounded Sequences / 13.:
Further Limit Theorems / 14.:
Divergent Sequences / 15.:
Monotone Sequences and the Number e / 16.:
Real Exponents / 17.:
The Bolzano-Weierstrass Theorem / 18.:
The Cauchy Condition / 19.:
The lim sup and lim inf of Bounded Sequences / 20.:
The lim sup and lim inf of Unbounded Sequences / 21.:
Infinite Series / V:
The Sum of an Infinite Series / 22.:
Algebraic Operations on Series / 23.:
Series with Nonnegative Terms / 24.:
The Alternating Series Test / 25.:
Absolute Convergence / 26.:
Power Series / 27.:
Conditional Convergence / 28.:
Double Series and Applications / 29.:
Limits of Real-Valued Functions and Continuous Functions on the Real Line / VI:
Definition of the Limit of a Function / 30.:
Limit Theorems for Functions / 31.:
One-Sided and Infinite Limits / 32.:
Continuity / 33.:
The Heine-Borel Theorem and a Consequence for Continuous Functions / 34.:
Metric Spaces / VII:
The Distance Function / 35.:
R[superscript n], l[superscript 2], and the Cauchy-Schwarz Inequality / 36.:
Sequences in Metric Spaces / 37.:
Closed Sets / 38.:
Open Sets / 39.:
Continuous Functions on Metric Spaces / 40.:
The Relative Metric / 41.:
Compact Metric Spaces / 42.:
The Bolzano-Weierstrass Characterization of a Compact Metric Space / 43.:
Continuous Functions on Compact Metric Spaces / 44.:
Connected Metric Spaces / 45.:
Complete Metric Spaces / 46.:
Baire Category Theorem / 47.:
Differential Calculus of the Real Line / VIII:
Basic Definitions and Theorems / 48.:
Mean-Value Theorems and L'Hospital's Rule / 49.:
Taylor's Theorem / 50.:
The Riemann-Stieltjes Integral / IX:
Riemann-Stieltjes Integration with Respect to an Increasing Integrator / 51.:
Riemann-Stieltjes Sums / 52.:
Riemann-Stieltjes Integration with Respect to an Arbitrary Integrator / 53.:
Functions of Bounded Variation / 54.:
Riemann-Stieltjes Integration with Respect to Functions of Bounded Variation / 55.:
The Riemann Integral / 56.:
Measure Zero / 57.:
A Necessary and Sufficient Condition for the Existence of the Riemann Integral / 58.:
Improper Riemann-Stieltjes Integrals / 59.:
Sequences and Series of Functions / X:
Pointwise Convergence and Uniform Convergence / 60.:
Integration and Differentiation of Uniformly Convergent Sequences / 61.:
Series of Functions / 62.:
Applications to Power Series / 63.:
Abel's Limit Theorems / 64.:
Summability Methods and Tauberian Theorems / 65.:
Transcendental Functions / XI:
The Exponential Function / 66.:
The Natural Logarithm Function / 67.:
The Trigonometric Functions / 68.:
Inner Product Spaces and Fourier Series / XII:
Normed Linear Spaces / 69.:
The Inner Product Space R[superscript 3] / 70.:
Inner Product Spaces / 71.:
Orthogonal Sets in Inner Product Spaces / 72.:
Periodic Functions / 73.:
Fourier Series: Definition and Examples / 74.:
Orthonormal Expansions in Inner Product Spaces / 75.:
Pointwise Convergence of Fourier Series in R[a, a + 2[pi] / 76.:
Cesaro Summability of Fourier Series / 77.:
Fourier Series in R[a, a + 2[pi] / 78.:
A Tauberian Theorem and an Application to Fourier Series / 79.:
Normed Linear Spaces and the Riesz Representation Theorem / XIII:
Normed Linear Spaces and Continuous Linear Transformations / 80.:
The Normed Linear Space of Continuous Linear Transformations / 81.:
The Dual Space of a Normed Linear Space / 82.:
Introduction to the Riesz Representation Theorem / 83.:
Proof of the Riesz Representation Theorem / 84.:
The Lebesgue Integral / XIV:
The Extended Real Line / 85.:
[sigma]-Algebras and Positive Measures / 86.:
Measurable Functions / 87.:
Integration on Positive Measure Spaces / 88.:
Lebesgue Measure on R / 89.:
Lebesgue Measure on [a, b] / 90.:
The Hilbert Spaces Y[superscript 2](X, M, [mu]) / 91.:
Vector Spaces / Appendix:
References
Hints to Selected Exercises
Index
Errata
Preface
Preface to the Dover Edition
Sets and Functions / I:
6.

図書

図書
by N. A. Šanin ; [translated from the Russian by E. Mendelson]
出版情報: Providence, R.I. : American Mathematical Society, 1968  iv, 325 p. ; 24 cm
シリーズ名: Translations of mathematical monographs ; v. 21
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7.

図書

図書
by Lester J. Heider , James E. Simpson
出版情報: Philadelphia : Saunders, c1967  xii, 379 p ; 24 cm
シリーズ名: Saunders mathematics books
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8.

図書

図書
K.G. Binmore
出版情報: Cambridge [Eng.] : Cambridge University Press, 1980  x, 130 p. ; 24 cm
シリーズ名: The foundations of analysis : a straightforward introduction / K.G. Binmore ; book 1
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目次情報: 続きを見る
Introduction
Proofs / 1:
Logic (I) / 2:
Logic (II) / 3:
Set operations / 4:
Relations / 5:
Functions / 6:
Real numbers (I) / 7:
Principle of induction / 8:
Real numbers (II) / 9:
Construction of the number systems / 10:
Number theory / 11:
Cardinality / 12:
Introduction
Proofs / 1:
Logic (I) / 2:
9.

図書

図書
J. Dieudonné
出版情報: New York : Academic Press, 1969  xviii, 387 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; v. 10 . Treatise on analysis / J. Dieudonné ; 1
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10.

図書

図書
Errett Bishop, Douglas Bridges
出版情報: Berlin ; New York : Springer-Verlag, c1985  xii, 477 p. ; 24 cm.
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 279
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