Notes on book "Measure Theory (2nd ed.) - Cohn Donald L."

Measure Thoery: Chp 7. Measures on Locally Compact Spaces

This chapter is devoted to the Riesz representation theorem and related results.

Locally Compact Spaces

A topological space is locally compact if each of its points has an open neighborhood whose closure is compact.

The Riesz representation Theorem

Theorem 7.2.8 (Riesz Representation Theorem). Let be a locally compact Hausdorff space, and let be a positive linear functional on . Then there is a unique regular Borel measure on such that

holds for each in .

Signed and Complex Measures; Duality

Additional Properties of Regular Measures

The -Measurable Sets and the Dual of

Products of Locally Compact Spaces

The Daniell-Stone Integral

References

[1] @book{cohn2013measure, title={Measure theory}, author={Cohn, Donald L}, year={2013}, publisher={Springer} }