| Description |
1 online resource |
| Series |
Oxford graduate texts in mathematics ; 8 |
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Oxford graduate texts in mathematics ; 8.
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| Contents |
Cover -- Titlepage -- Copyright -- Dedication -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- 1 Measures -- 1.1 Measurable sets and functions -- 1.2 Positive measures -- 1.3 Integration of non-negative measurable functions -- 1.4 Integrable functions -- 1.5 Lp-spaces -- 1.6 Inner product -- 1.7 Hilbert space: a first look -- 1.8 The Lebesgue-Radon-Nikodym theorem -- 1.9 Complex measures -- 1.10 Convergence -- 1.11 Convergence on finite measure space -- 1.12 Distribution function -- 1.13 Truncation -- Exercises -- 2 Construction of measures -- 2.1 Semi-algebras |
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2.2 Outer measures -- 2.3 Extension of measures on algebras -- 2.4 Structure of measurable sets -- 2.5 Construction of Lebesgue-Stieltjes measures -- 2.6 Riemann vs. Lebesgue -- 2.7 Product measure -- Exercises -- 3 Measure and topology -- 3.1 Partition of unity -- 3.2 Positive linear functionals -- 3.3 The Riesz-Markov representation theorem -- 3.4 Lusin's theorem -- 3.5 The support of a measure -- 3.6 Measures on Rk -- differentiability -- Exercises -- 4 Continuous linear functionals -- 4.1 Linear maps -- 4.2 The conjugates of Lebesgue spaces -- 4.3 The conjugate of Cc(X) |
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4.4 The Riesz representation theorem -- 4.5 Haar measure -- Exercises -- 5 Duality -- 5.1 The Hahn-Banach theorem -- 5.2 Reflexivity -- 5.3 Separation -- 5.4 Topological vector spaces -- 5.5 Weak topologies -- 5.6 Extremal points -- 5.7 The Stone-Weierstrass theorem -- 5.8 Operators between Lebesgue spaces: Marcinkiewicz's interpolation theorem -- 5.9 Fixed points -- 5.10 The bounded weak*-topology -- Exercises -- 6 Bounded operators -- 6.1 Category -- 6.2 The uniform boundedness theorem -- 6.3 The open mapping theorem -- 6.4 Graphs -- 6.5 Quotient space -- 6.6 Operator topologies -- Exercises |
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7 Banach algebras -- 7.1 Basics -- 7.2 Commutative Banach algebras -- 7.3 Involutions and C*-algebras -- 7.4 Normal elements -- 7.5 The Arens products -- Exercises -- 8 Hilbert spaces -- 8.1 Orthonormal sets -- 8.2 Projections -- 8.3 Orthonormal bases -- 8.4 Hilbert dimension -- 8.5 Isomorphism of Hilbert spaces -- 8.6 Direct sums -- 8.7 Canonical model -- 8.8 Tensor products -- 8.8.1 An interlude: tensor products of vector spaces -- 8.8.2 Tensor products of Hilbert spaces -- Exercises -- 9 Integral representation -- 9.1 Spectral measure on a Banach subspace -- 9.2 Integration -- 9.3 Case Z=X |
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9.4 The spectral theorem for normal operators -- 9.5 Parts of the spectrum -- 9.6 Spectral representation -- 9.7 Renorming method -- 9.8 Semi-simplicity space -- 9.9 Resolution of the identity on Z -- 9.10 Analytic operational calculus -- 9.11 Isolated points of the spectrum -- 9.12 Compact operators -- Exercises -- 10 Unbounded operators -- 10.1 Basics -- 10.2 The Hilbert adjoint -- 10.3 The spectral theorem for unbounded selfadjoint operators -- 10.4 The operational calculus for unbounded selfadjoint operators -- 10.5 The semi-simplicity space for unbounded operators in Banach space |
| Summary |
"This book explores this developer's dilemma or 'Kuznetsian tension' between structural transformation and income inequality. Developing countries are seeking economic development--that is, structural transformation--which is inclusive in the sense that it is broad-based and raises the income of all, especially the poor. Thus, inclusive economic growth requires steady, or even falling, income inequality if it is to maximize the growth of incomes at the lower end of the distribution. Yet, this is at odds with Simon Kuznets hypothesis that economic development tends to put upward pressure on income inequality, at least initially and in the absence of countervailing policies. The book asks: what are the types or 'varieties' of structural transformation that have been experienced in developing countries? What inequality dynamics are associated with each variety of structural transformation? And what policies have been utilized to manage trade-offs between structural transformation, income inequality, and inclusive growth? The book answers these questions using a comparative case study approach, contrasting nine developing countries while employing a common analytical framework and a set of common datasets across the case studies. The intended intellectual contribution of the book is to provide a comparative analysis of the relationship between structural transformation, income inequality, and inclusive growth; to do so empirically at a regional and national level; and to draw conclusions from the cases on the varieties of structural transformation, their inequality dynamics, and the policies that have been employed to mediate the developer's dilemma"--Publisher's description |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Description based on online resource; title from home page (Oxford Academic, viewed on September 8, 2023) |
| Subject |
Mathematical analysis.
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Mathematical analysis
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| Form |
Electronic book
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| Author |
Viselter, Ami, author.
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| ISBN |
0191944653 |
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9780191944659 |
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9780192666192 |
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0192666193 |
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