Measure Theory and Fine Properties of Functions: Studies in Advanced Mathematics
Autor Lawrence Craig Evans, Ronald F. Gariepyen Limba Engleză Hardback – 18 dec 1991
The text provides complete proofs of many key results omitted from other books, including Besicovitch's Covering Theorem, Rademacher's Theorem (on the differentiability a.e. of Lipschitz functions), the Area and Coarea Formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Alexandro's Theorem (on the twice differentiability a.e. of convex functions).
Topics are carefully selected and the proofs succinct, but complete, which makes this book ideal reading for applied mathematicians and graduate students in applied mathematics.
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Specificații
ISBN-13: 9780849371578
ISBN-10: 0849371570
Pagini: 280
Ilustrații: 1, black & white illustrations
Dimensiuni: 165 x 236 x 23 mm
Greutate: 0.54 kg
Ediția:New.
Editura: Taylor & Francis Us
Seriile Studies in Advanced Mathematics, Mathematical Chemistry Series
ISBN-10: 0849371570
Pagini: 280
Ilustrații: 1, black & white illustrations
Dimensiuni: 165 x 236 x 23 mm
Greutate: 0.54 kg
Ediția:New.
Editura: Taylor & Francis Us
Seriile Studies in Advanced Mathematics, Mathematical Chemistry Series
Public țintă
Applied mathematicians and graduate students interested in applied mathematicsCuprins
GENERAL MEASURE THEORY
Measures and Measurable Functions
Lusin's and Egoroff's Theorems
Integrals and Limit Theorems
Product Measures, Fubini's Theorem, Lebesgue Measure
Covering Theorems
Differentiation of Radon Measures
Lebesgue Points
Approximate continuity
Riesz Representation Theorem
Weak Convergence and Compactness for Radon Measures
HAUSDORFF MEASURE
Definitions and Elementary Properties; Hausdorff Dimension
Isodiametric Inequality
Densities
Hausdorff Measure and Elementary Properties of Functions
AREA AND COAREA FORMULAS
Lipschitz Functions, Rademacher's Theorem
Linear Maps and Jacobians
The Area Formula
The Coarea Formula
SOBOLEV FUNCTIONS.
Definitions And Elementary Properties. Approximation
Traces. Extensions. Sobolev Inequalities
Compactness. Capacity
Quasicontinuity; Precise Representations of Sobolev Functions. Differentiability on Lines
BV FUNCTIONS AND SETS OF FINITE PERIMETER
Definitions and Structure Theorem
Approximation and Compactness
Traces. Extensions. Coarea Formula for BV Functions. Isoperimetric Inequalities.
The Reduced Boundary
The Measure Theoretic Boundary; Gauss-Green Theorem. Pointwise Properties of BV Functions
Essential Variation on Lines
A Criterion for Finite Perimeter. DIFFERENTIABILITY AND APPROXIMATION BY C1 FUNCTIONS.
Lp Differentiability a.e.; Approximate Differentiability
Differentiability A.E. for W1,P (P > N). Convex Functions
Second Derivatives a.e. for convex functions
Whitney's Extension Theorem
Approximation by C1 Functions
NOTATION
REFERENCES
Measures and Measurable Functions
Lusin's and Egoroff's Theorems
Integrals and Limit Theorems
Product Measures, Fubini's Theorem, Lebesgue Measure
Covering Theorems
Differentiation of Radon Measures
Lebesgue Points
Approximate continuity
Riesz Representation Theorem
Weak Convergence and Compactness for Radon Measures
HAUSDORFF MEASURE
Definitions and Elementary Properties; Hausdorff Dimension
Isodiametric Inequality
Densities
Hausdorff Measure and Elementary Properties of Functions
AREA AND COAREA FORMULAS
Lipschitz Functions, Rademacher's Theorem
Linear Maps and Jacobians
The Area Formula
The Coarea Formula
SOBOLEV FUNCTIONS.
Definitions And Elementary Properties. Approximation
Traces. Extensions. Sobolev Inequalities
Compactness. Capacity
Quasicontinuity; Precise Representations of Sobolev Functions. Differentiability on Lines
BV FUNCTIONS AND SETS OF FINITE PERIMETER
Definitions and Structure Theorem
Approximation and Compactness
Traces. Extensions. Coarea Formula for BV Functions. Isoperimetric Inequalities.
The Reduced Boundary
The Measure Theoretic Boundary; Gauss-Green Theorem. Pointwise Properties of BV Functions
Essential Variation on Lines
A Criterion for Finite Perimeter. DIFFERENTIABILITY AND APPROXIMATION BY C1 FUNCTIONS.
Lp Differentiability a.e.; Approximate Differentiability
Differentiability A.E. for W1,P (P > N). Convex Functions
Second Derivatives a.e. for convex functions
Whitney's Extension Theorem
Approximation by C1 Functions
NOTATION
REFERENCES