General Integration and Measure

This is a sequel to Dr Weir's undergraduate textbook on Lebesgue Integration and Measure.

This is a sequel to Dr Weir's undergraduate textbook on Lebesgue Integration and Measure (CUP. 1973) in which he provided a concrete approach to the Lebesgue integral in terms of step functions and went on from there to deduce the abstract concept of Lebesgue measure. In this second volume, the treatment of the Lebesgue integral is generalised to give the Daniell integral and the related general theory of measure. This approach via integration of elementary functions is particularly well adapted to the proof of Riesz's famous theorems about linear functionals on the classical spaces C (X) and LP and also to the study of topological notions such as Borel measure. This book will be used for final year honours courses in pure mathematics and for graduate courses in functional analysis and measure theory.

Preface; 8. General Integration; 9. Lebesgue-Stieltjes integrals and measures; 10. The Riesz representation theorem; 11. General measures; 12. The classical approach; 13. Uniqueness and approximation theorems; 14. Product measures; 15. Borel measures; 16. Real and complex measures; 17. The Radon-Nikodym theorem; Appendix; Solutions; References; Index.

This is a sequel to Dr Weir's undergraduate textbook on Lebesgue Integration and Measure (CUP 1973) in which he provided a concrete approach to the Lebesgue integral in terms of step functions and went on from there to deduce the abstract concept of Lebesgue measure. In this second volume, the treatment of the Lebesgue integral is generalised to give the Daniell integral and the related general theory of measure.