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1.

図書

図書
by Adriaan C. Zaanen
出版情報: Amsterdam : North-Holland Pub. Co., 1961  ix, 254 p. ; 23 cm
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2.

図書

図書
Robert R. Phelps
出版情報: Berlin ; New York : Springer-Verlag, c2001  124 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1757
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3.

図書

図書
Elias M. Stein & Rami Shakarchi
出版情報: Princeton, N.J. ; Oxford : Princeton University Press, c2005  xix, 402 p ; 24 cm
シリーズ名: Princeton lectures in analysis ; 3
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4.

図書

図書
George G. Roussas
出版情報: Amsterdam ; Tokyo : Elsevier Academic Press, c2005  xviii, 443 p. ; 24 cm
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目次情報: 続きを見る
Preface
Certain Classes of Sets, Measurability, Pointwise Approximation / 1:
Definition and Construction of a Measure and Its Basic Properties / 2:
Some Modes of Convergence of a Sequence of Random Variables and Their Relationships / 3:
The Integral of a Random Variable and Its Basic Properties / 4:
Standard Convergence Theorems, The Fubini Theorem / 5:
Standard Moment and Probability Inequalities, Convergence in the r-th Mean and Its Implications / 6:
The Hahn-Jordan Decomposition Theorem, The Lebesgue Decomposition Theorem, and The Radon-Nikcodym Theorem / 7:
Distribution Functions and Their Basic Properties, Helly-Bray Type Results / 8:
Conditional Expectation and Conditional Probability, and Related Properties and Results / 9:
Independence / 10:
Topics from the Theory of Characteristic Functions / 11:
The Central Limit Problem: The Centered Case / 12:
The Central Limit Problem: The Noncentered Case / 13:
Topics from Sequences of Independent Random Variables / 14:
Topics from Ergodic Theory / 15:
Preface
Certain Classes of Sets, Measurability, Pointwise Approximation / 1:
Definition and Construction of a Measure and Its Basic Properties / 2:
5.

図書

図書
V.I. Bernik, M.M. Dodson
出版情報: Cambridge [Cambridgeshire] : Cambridge University Press, 1999  xi, 172 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; v. 137
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目次情報: 続きを見る
Preface
Notation
Diophantine approximation and manifolds / Chapter 1.:
Introduction / 1.1.:
Diophantine approximation in one dimension / 1.2.:
Approximation in higher dimensions / 1.3.:
Euclidean submanifolds / 1.4.:
Metric Diophantine approximation on manifolds / 1.5.:
Notes / 1.6.:
Khintchine's and Groshev's theorems for manifolds / Chapter 2.:
Extremal manifolds / 2.1.:
Khintchine and Groshev type manifolds / 2.3.:
Baker's conjecture / 2.4.:
Higher dimensional manifolds / 2.5.:
Hausdorff measure and dimension / 2.6.:
Hausdorff measure / 3.1.:
Hausdorff dimension / 3.3.:
Properties of Hausdorff dimension / 3.4.:
Determining the Hausdorff dimension / 3.5.:
Hausdorff dimension on manifolds / 3.6.:
Upper bounds for Hausdorff dimension / 3.7.:
Diophantine approximation on manifolds / 4.1.:
Smooth manifolds of dimension at least 2 / 4.3.:
Simultaneous Diophantine approximation / 4.4.:
Lower bounds for Hausdorff dimension / 4.5.:
Regular systems / 5.1.:
Ubiquitous systems / 5.3.:
Simultaneous Diophantine approximation on manifolds / 5.4.:
Diophantine approximation over the p-adic field / 5.5.:
Introduction to p-adic numbers / 6.1.:
Diophantine approximation in Q[subscript p] / 6.2.:
Integral polynomials with small p-adic values / 6.3.:
Applications / 6.4.:
Diophantine type and very well approximable numbers / 7.1.:
A wave equation / 7.3.:
The rotation number / 7.4.:
Dynamical systems / 7.5.:
Linearising diffeomorphisms / 7.6.:
Diophantine approximation in hyperbolic space / 7.7.:
References / 7.8.:
Index
Preface
Notation
Diophantine approximation and manifolds / Chapter 1.:
6.

図書

図書
Graham Everest, Thomas Ward
出版情報: London ; New York ; Tokyo : Springer, c1999  xii, 211 p. ; 24 cm
シリーズ名: Universitext
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7.

図書

図書
Gerald A. Edgar
出版情報: New York, NY : Springer, c1998  x, 286 p. ; 25 cm
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8.

図書

図書
Klaus Bichteler
出版情報: Basel ; Boston : Birkhäuser, c1998  viii, 193 p. ; 24 cm
シリーズ名: Birkhäuser advanced texts : Basler Lehrbücher / edited by Herbert Amann, Hanspeter Kraft
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9.

図書

図書
by Corneliu Constantinescu ... [et al.]
出版情報: Dordrecht : Kluwer Academic Publishers, c1998  ix, 861 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 454
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目次情報: 続きを見る
Preface
Acknowledgements
Introduction
Suggestions to the Reader
Preliminaries / 0:
Vector Lattices / 1:
Ordered Vector Spaces / 1.1:
Substructures, Quotients, Products / 1.2:
Bands and Orthogonality / 1.4:
Homomorphisms / 1.5:
The Order Dual of a Vector Lattice / 1.6:
Continuous Functionals / 1.7:
Order and Topology / 1.8:
Metric Spaces and Banach Spaces / 1.9:
Banach Lattices / 1.10:
Hilbert Lattices / 1.11:
Lattice Products / 1.12:
Elementary Integration Theory / 2:
Riesz Lattices / 2.1:
Daniell Spaces / 2.2:
The Closure of a Daniell Space / 2.3:
The Integral for a Daniell Space / 2.4:
Systems of Sets, Step Functions, and Stone Lattices / 2.5:
Positive Measures / 2.6:
Closure, Completion, and Integrals for Positive Measure Spaces / 2.7:
Measurable Spaces and Measurability / 2.8:
Measurability versus Integrability / 2.9:
Stieltjes Functionals and Stieltjes Measures. Lebesgue Measure / 2.10:
L[superscript p]-Spaces / 3:
Classes modulo [mu] and Convergence in Measure / 3.1:
The Holder and Minkowski Inequalities and the L[superscript p]-Spaces / 3.2:
L[superscript p]-Spaces for 0 [ p [ [infinity] / 3.3:
Uniform integrability and the Generalized Lebesgue Convergence Theorem / 3.4:
Localization / 3.5:
Products and L[superscript [infinity]] / 3.6:
Real Measures / 4:
Nullcontinuous Functionals / 4.1:
Real Measures and Spaces of Real Measures / 4.2:
Integrals for Real Measures / 4.3:
Bounded Measures / 4.4:
Atomic and Atomless Measures / 4.5:
The Radon-Nikodym Theorem. Duality / 5:
Absolute Continuity / 5.1:
The Theorem of Radon-Nikodym / 5.2:
Duality for Function Spaces / 5.3:
The Classical Theory of Real Functions / 6:
Functions of Locally Finite Variation / 6.1:
Real Stieltjes Measures / 6.2:
Absolutely Continuous Functions / 6.3:
Vitali's Covering Theorem / 6.4:
Differentiable Functions / 6.5:
Spaces of Multiply Differentiable Functions / 6.6:
Riemann-Stieltjes Integrals / 6.7:
Historical Remarks
Name Index
Subject Index
Symbol Index
Preface
Acknowledgements
Introduction
10.

図書

図書
K. Hinderer
出版情報: Berlin ; New York : Springer-Verlag, 1972  vii, 247 p. ; 26 cm
シリーズ名: Hochschultext
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