Lebesgue Integration On Euclidean Space Jones Pdf 17

[Amabella Tevebaugh]

Terence Tao's An Introduction to Measure Theory. I like his exposition very much as he first constructs the Jordan measure (which is very intuitive if one is used to idea that one can calculate the area of a set by "approximating" it with sets of a more elementary nature like squares or polygons). He then connects the Jordan measure to the Riemann Integral and explains why there is a need to develop a more general (lebesgue) measure/Integral. He then moves on to integration theory and defines the lebesgue integral. Once you have struggled through the first sections of the book and gotten used to the ideas presented there, I think the leap to abstract measure space theory (which is presented in one of the sections) is short. The rest of the book is devoted to convergence/differentiation theorems and construction of measures. What I liked with the book is that he does not start off with abstract measure theory, constructions of measures (like Caratheodorys theorem) and all that without little or no motivation. Another nice feature is that he leaves many of the easy propositions as exercises. Also, last but not least, there is a very nice section on problem solving techniques, which could be very useful.

lebesgue integration on euclidean space jones pdf 17

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