## MAT 324: Real Analysis
## Stony Brook Fall 2017 |
---|

Instructor |
Aleksey Zinger | OHs: Tu 2:30-4pm, Th 11:30am-1pm in Math 3-111 |

TA |
Yuhan Sun | OHs: W 4-5pm in Math 5-125B, 5-7pm in MLC |

Math Learning Center (MLC) |

Date |
Topic | Read |
Problem Set |

8/29, Tu | Review and introduction | Chapter 1 | #1 solutions |

8/31, Th | Outer measure | Sections 2.1,2.2 | |

9/5, Tu | no class, no office hours | ||

9/7, Th | Measurable subsets | Section 2.3, p302 | #2 solutions |

9/12, Tu | Properties of measurable subsets | Sections 2.3,2.4 | |

9/14, Th | Measure spaces, Borel sets | Sections 2.4,2.5 | |

9/19, Tu | Probability spaces, measurable functions | Sections 2.5-2.7,3.1-3.3 | #3 solutions |

9/21, Th | Properties of measurable functions | Sections 3.3,3.4 | |

9/26, Tu | Probability distributions | Sections 3.4-3.6 | #4 solutions |

9/28, Th | Lebesgue integral | Section 4.1 | |

10/03, Tu | Monotone convergence | Section 4.2 | #5 solutions |

10/05, Th | Integrable functions | Section 4.3 | |

10/10, Tu | Dominated convergence | Section 4.4 | #6 solutions |

10/12, Th | Riemann vs. Lebesgue integration | Sections 4.5,4.6 | |

10/17, Tu | Approximating measurable functions | Sections 4.6-4.8 | bonus solutions |

10/19, Th |
midterm in class:exam,
solutions | ||

10/24, Tu | The Banach spaces L^{p} |
Sections 5.1,5.3 | #7 solutions |

10/26, Th | |||

10/31, Tu | Modes of convergence | Sections 8.1,5.2 | #8 solutions |

11/02, Th | The Hilbert space L^{2} |
Sections 5.2,5.4,5.5 | |

11/07, Tu | Inner-product spaces | Section 5.2 | #9 solutions |

11/09, Th | Product measure spaces | Section 6.1-6.3 pp160-164 in here | |

11/14, Tu | Fubini's Theorems | Sections 6.4-6.6 pp164-170 in here |
#10 |

11/16, Th | |||

11/21, Th | |||

11/23, Th | no class, no office hours | ||

11/28, Tu | Radon-Nikodym Theorem | Sections 7.1,7.2 | |

11/30, Th | |||

12/5, Tu | Discussion/review |
everything | |

12/7, Th | |||

12/15, F | final exam, 11:15am-1:45pm |

This page is maintained by Aleksey Zinger.