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56,05 ۥ 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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