# Course

## M301 - Lebesgue Integration

Course No:
M301
Credit:
4
Prerequisites:
M201
Approval:
2014
UG-Core
Syllabus:
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.
Text Books:
1. H. L. Royden, “Real Analysis”, Prentice-Hall of India, 2012.
2. G. B. Folland, “Real Analysis”, Wiley-Interscience Publication, John Wiley & Sons, 1999.
Reference Books:
1. G. de Barra, “Measure Theory and Integration”, New Age International, New Delhi, 2003.
2. W. Rudin, “Principles of Mathematical Analysis”, Tata McGraw-Hill, 2013.