000			01844nam a22002057a 4500
003			OSt
005			20241106161159.0
008			190124b ||||| |||| 00| 0 eng d
020			_a978-1-4704-1099-5
040			_cSurya Book Supplier _aICTS-TIFR
050			_aQA300
100			_aSimon Barry
245			_aReal analysis _b: a comprehensive course in analysis part 1
260			_aRhode Island: _bAmerican Mathematical Society, _c[c2015]
300			_a789 p
505			_aChapter 1. Preliminaries Chapter 2. Topological spaces Chapter 3. A first look at Hilbert spaces and Fourier series Chapter 4. Measure theory Chapter 5. Convexity and Banach spaces Chapter 6. Tempered distributions and the Fourier transform Chapter 7. Bonus chapter: Probability basics Chapter 8. Bonus chapter: Hausdorff measure and dimension Chapter 9. Bonus chapter: Inductive limits and ordinary distributions
520			_aPart 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and Lp spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory. --- summary provided by publisher
650			_aMathematics
942			_2lcc _cBK
999			_c2191 _d2191