#resources/textbooks
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Rudin: Real and complex analysis
Good general reference but the following books have more useful techniques
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Stein and Shakarchi: Real analysis.
Does not have \(L^p\) spaces. A good source for this and convexity is Lieb-Loss: Analysis, Chapter 2.
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Stein and Shakarchi: Fourier Analysis.
This book is very elementary but more than sufficient chapters 2 and 3 are Fourier series, chapter 5 is Fourier transform.
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Evans: Partial Differential Equations. Chapter 5.
For Sobolev spaces
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Shiryayev: Probability.
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Feller: An Introduction To Probability Theory And Its Applications
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Durrett: Probability: Theory And Examples