**MTH 535 Measure Theory and Integration**

Department of Mathematics, University of Rhode Island

Instructor |
Orlando Merino, merino@math.uri.edu, 874-4442, Lippitt Hall 101C |

Meets |
M, W 3 p.m. Lippitt Hall 201 |

Text |
Adams, M. and Guillemin, V., Measure Theory and Probability, latest Edition, Birkauser, Boston, supplemented by handouts |

Prerequisites |
MTH 435-436 or permission of the instructor |

About the Course |
This course is part II of an introduction to real analysis at the graduate level, particularly integration theory and its applications to Fourier analysis, probability theory and other mathematical areas. This course can be regarded as a continuation of MTH 435-436 with the same level of rigor. It should useful to well-prepared students of electrical engineering, physics or statistics as well as students of mathematics. Topics: Hahn decomposition, Lebesgue-Radon-Nikodym theorem, review of metric spaces, L1, L2, Hilbert space, Fourier series, Fourier integrals, applications, invariant measures, Birkhoff Ergodic Theorem, Random variables and stochastic processes, Brownian motion, other topics may be covered depending on interest. |

Evaluation |
Homework (50%), Midterm Exam (20%), Final Exam (30%) |