Measure Theory and Integration Michael E. Taylor
Publisher: American Mathematical Society

Nandakumaran from the Indian Institute of Sciences began the series of lectures with an exposition on the analysis and limitations of Riemann integration. IMC: Practice Leads Theory ends by pointing out the challenges these differences present when trying to measure the effectiveness of IMC. This abstract unifying framework enables one to rigorously 'measure' quantities over a space, and also enable integration. As the word “measure" indicates, measure theory is something which deals with measures of some objects. Measure Theory and Integration. (I'd be willing to learn PDEs, but I'm not up for going through the Probability and Measure Theory book I have, as Brownian Motion is at the very end) As a note, I've taken measure theory. Theorem, Borel and Lebesque measures, measurable functions, Lebesque integration, convergence theorems, Lp spaces, general measure and integration theory, Radon-Nikodyn theorem, Fubini theorem, Lebesque-Stieltjes integration. Measure theory broadens our vision about probability, random events, random variables and integration. It also allows elegant notation for probability theory. Real Analysis Measure Theory, Integration, & Hilbert Spaces.