• Measure and Outer Measure • Construction of Outer Measures • Metric Outer Measures and Borel Outer Measures • Hausdorff Measures • Hausdorff Measures on Linear Spaces • Covering Theorems in a Metric Space • Differentiation of Measures • Averaging Operators and Differentiation of Integrals • Lebesgue Differentiation Theorem for Integrals • Hardy-Littlewood Maximal Functions • Density of Sets • Approximate Limit and Approximate Continuity • Lipschitz Mappings • Integration with Respect to a Measure on a Metric Space
Measure and metric are two fundamental concepts in measuring the size of a mathematical object. Yet there has been no systematic investigation of this relation. The book closes this gap.
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