Chapter 11: Measure Spaces

111
s-algebras

Definition of s-algebra; countable sets; s-algebra
generated by a family of sets; Borel s-algebras.

112
Measure spaces

Definition of measure space; the use of ¥; elementary
properties; negligible sets; image measures.

113
Outer measures and Carathéodory's construction

Outer measures; Carathéodory's construction of a measure from an
outer measure.

114
Lebesgue measure on **R**

Half-open intervals; Lebesgue outer measure; Lebesgue measure;
Borel sets are measurable.

115
Lebesgue measure on **R**^{r}

Half-open intervals; Lebesgue outer measure; Lebesgue measure;
Borel sets are measurable.

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Revised 22.7.05