Measure Theory · Number
Sigma-Algebras and Measurable Sets
The σ-algebra is the domain on which a measure is defined. Vitali’s construction shows that measure cannot be assigned consistently to every subset of ℝ.
WHAT STUDENTS WILL LEARN
✓Define σ-algebras and verify examples
✓Construct the Borel σ-algebra
✓Define measurable functions
✓Understand why non-measurable sets exist (Vitali)
BUILDS ON
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