Course In Analysis A V3 - JACOB NIELS

In This Third Volume Of A Course In Analysisquot;, Two Topics Indispensible For Every Mathematician Are Treated: Measure And Integration Theory; And Complex Function The First Part Measurable Spaces And Measure Spaces Are Introduced And Caratheodory's Extension Theorem Is Proved. This Is Followed By The Construction Of The Integral With Respect To A Measure, In Particular With Respect To The Lebesgue Measure In The Euclidean Space. The Radonndash;nikodym Theorem And The Transformation Theorem Are Discussed And Much Care Is Taken To Handle Convergence Theorems With Applications, As Well As Lp-spaces.integration On Product Spaces And Fubini's Theorem Is A Further Topic As Is The Discussion Of The Relation Between The Lebesgue Integral And The Riemann Integral.