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電子ブック
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1. Probability Theory with Applications. Second Edition
by M. M. Rao, R. J. Swift
出版情報: Boston, MA : Springer Science+Business Media, Inc., 2006
シリーズ名: Mathematics and Its Applications ; 582
オンライン: http://dx.doi.org/10.1007/0-387-27731-5
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電子ブック
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2. Real Analysis: Measures, Integrals and Applications
by Boris Makarov, Anatolii Podkorytov
出版情報: London : Springer London : Imprint: Springer, 2013
シリーズ名: Universitext ;
オンライン: http://dx.doi.org/10.1007/978-1-4471-5122-7
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Measure
The Lebesgue Model
Measurable Functions
The Integral
The Product Measure
Change of Variables in an Integral
Integrals Dependent on a Parameter
Surface Integrals
Approximation and Convolution of the Space
Fourier Series and the Fourier Transform
Charges. The Radon-Nikodym Theory
Integral Representation of Linear Functionals
Appendices
Measure
The Lebesgue Model
Measurable Functions
3.

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3. Measure, Integral, Derivative : A Course on Lebesgue's Theory
by Sergei Ovchinnikov
出版情報: New York, NY : Springer New York : Imprint: Springer, 2013
シリーズ名: Universitext ;
オンライン: http://dx.doi.org/10.1007/978-1-4614-7196-7
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1 Preliminaries
2 Lebesgue Measure
3  Lebesgue Integration
4 Differentiation and Integration
A Measure and Integral over Unbounded Sets
Index
1 Preliminaries
2 Lebesgue Measure
3  Lebesgue Integration
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4. Introduction to Mathematical Analysis
by Igor Kriz, Aleš Pultr
出版情報: Basel : Springer Basel : Imprint: Birkhäuser, 2013
オンライン: http://dx.doi.org/10.1007/978-3-0348-0636-7
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Preface
Introduction
Part 1. A Rigorous Approach to Advanced Calculus
1. Preliminaries
2. Metric and Topological Spaces I
3. Multivariable Differential Calculus
4. Integration I: Multivariable Riemann Integral and Basic Ideas toward the Lebesgue Integral
5. Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration
6. Systems of Ordinary Differential Equations
7. System of Linear Differential Equations
8. Line Integrals and Green's Theorem
Part 2. Analysis and Geometry
9. An Introduction to Complex Analysis
10. Metric and Topological Spaces II
11. Multilinear Algebra
12. Smooth Manifolds, Differential Forms and Stokes' Theorem
13. Calculus of Variations and the Geodesic Equation
14. Tensor Calculus and Riemannian Geometry
15. Hilbert Spaces I: Definitions and Basic Properties
16. Hilbert Spaces II: Examples and Applications
Appendix A. Linear Algebra I: Vector Spaces
Appendix B. Linear Algebra II: More about Matrices
Bibliography
Index of Symbols
Index.
Preface
Introduction
Part 1. A Rigorous Approach to Advanced Calculus
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5. Geometric Measure Theory and Real Analysis
edited by Luigi Ambrosio
出版情報: Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale, 2014
シリーズ名: Publications of the Scuola Normale Superiore ; 17
オンライン: http://dx.doi.org/10.1007/978-88-7642-523-3
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Vladimir I. Bogachev: Sobolev classes on infinite-dimensional spaces
Roberto Monti: Isoperimetric problem and minimal surfaces in the Heisenberg group
Emanuele Spadaro: Regularity of higher codimension area minimizing integral currents
Davide Vittone: The regularity problem for sub-Riemannian geodesics
Vladimir I. Bogachev: Sobolev classes on infinite-dimensional spaces
Roberto Monti: Isoperimetric problem and minimal surfaces in the Heisenberg group
Emanuele Spadaro: Regularity of higher codimension area minimizing integral currents
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6. Topics on Concentration Phenomena and Problems with Multiple Scales
edited by Andrea Braides, Valeria Chiadò Piat
出版情報: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2006
シリーズ名: Lecture Notes of the Unione Matematica Italiana ; 2
オンライン: http://dx.doi.org/10.1007/978-3-540-36546-4
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7. Measure, Topology, and Fractal Geometry
edited by Gerald Edgar
出版情報: New York, NY : Springer Science+Business Media, LLC, 2008
シリーズ名: Undergraduate Texts in Mathematics ;
オンライン: http://dx.doi.org/10.1007/978-0-387-74749-1
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8. Real Analysis: Foundations. 1st ed. 2021
by Sergei Ovchinnikov
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2021
シリーズ名: Universitext ;
オンライン: https://doi.org/10.1007/978-3-030-64701-8
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1 Rational Numbers
2 Real Numbers
3 Continuous Functions
4 Differentiation
5 Integration
6 Infinite Series
A Natural Numbers and Integers
B Dedekind's Construction of Real Numbers. C A Panorama of Ordered Fields
1 Rational Numbers
2 Real Numbers
3 Continuous Functions
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9. Combined Measure and Shift Invariance Theory of Time Scales and Applications. 1st ed. 2022
by Chao Wang, Ravi P. Agarwal
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2022
シリーズ名: Developments in Mathematics ; 77
オンライン: https://doi.org/10.1007/978-3-031-11619-3
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Riemann Integration, Stochastic Calculus and Shift Operators on Time Scales
♢α-Measurability and Combined Measure Theory on Time Scales
Shift Invariance and Matched Spaces of Time Scales
Almost Periodic Functions under Matched Spaces of Time Scales
Almost Automorphic Functions under Matched Spaces of Time Scales
C0-Semigroup and Stepanov-like Almost Automorphic Functions on Hybrid Time Scales
Almost Periodic Dynamic Equations under Matched Spaces
Almost Automorphic Dynamic Equations under Matched Spaces
Applications on Dynamics Models under Matched Spaces
Riemann Integration, Stochastic Calculus and Shift Operators on Time Scales
♢α-Measurability and Combined Measure Theory on Time Scales
Shift Invariance and Matched Spaces of Time Scales
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10. A Second Course in Analysis. 1st ed. 2022
by M. Ram Murty
出版情報: Singapore : Springer Nature Singapore : Imprint: Springer, 2022
シリーズ名: IMSc Lecture Notes in Mathematics ;
オンライン: https://doi.org/10.1007/978-981-16-7246-0
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1. Background
2. Measure Theory
3. Fourier Transforms
4. Complex Analysis
5. Introduction to Algebraic Topology
Index
1. Background
2. Measure Theory
3. Fourier Transforms