Outer measure, measurable sets, Lebesgue measure, measurable functions, Lebesgue integral, Basic properties of Lebesgue integral, convergence in measure, differentiation and Lebesgue measure. L p Spaces, Holder and Minkowski inequalities, Riesz-Fisher theorem, Radon-Nykodin theorem, Riesz representation theorem. Fourier series, L 2 -convergence properties of Fourier series, Fourier transform and its properties.
- H. L. Royden, “Real Analysis”, Prentice-Hall of India, 2012.
- G. B. Folland, “Real Analysis”, Wiley-Interscience Publication, John Wiley & Sons, 1999.
- G. de Barra, “Measure Theory and Integration”, New Age International, New Delhi, 2003.
- W. Rudin, “Principles of Mathematical Analysis”, Tata McGraw-Hill, 2013.