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This graduate-level course covers Lebesgue’s integration theory with applications to analysis, including an introduction to convolution and the Fourier transform. This course will focus on the abstract measure theory and the Lebesgue integral. We will begin by defining the Lebesgue integral, prove the main convergence theorems, and construct Lebesgue measure in Rn. Other topics include Lp- spaces, Fubini Theorem, and the Area and Coarea Formulas.
Assessment
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
Certification
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Course Credit: MIT
Course Curriculum
Module: 01 | |||
Measure and Integration lec1 | 00:05:00 | ||
Measure and Integration lec2 | 00:05:00 | ||
Measure and Integration lec3 | 00:05:00 | ||
Measure and Integration lec4 | 00:05:00 | ||
Measure and Integration lec5 | 00:10:00 | ||
Measure and Integration lec6 | 00:05:00 | ||
Module: 02 | |||
Measure and Integration lec7 | 00:05:00 | ||
Measure and Integration lec8 | 00:05:00 | ||
Measure and Integration lec9 | 00:05:00 | ||
Measure and Integration lec10 | 00:10:00 | ||
Measure and Integration lec11 | 00:05:00 | ||
Measure and Integration lec12 | 00:05:00 | ||
Module: 03 | |||
Measure and Integration lec13 | 00:05:00 | ||
Measure and Integration lec14 | 00:05:00 | ||
Measure and Integration lec15 | 00:10:00 | ||
Measure and Integration lec16 | 00:05:00 | ||
Measure and Integration lec17 | 00:05:00 | ||
Measure and Integration lec18 | 00:10:00 | ||
Module: 04 | |||
Measure and Integration lec19 | 00:05:00 | ||
Measure and Integration lec20 | 00:05:00 | ||
Measure and Integration lec21 | 00:05:00 | ||
Measure and Integration lec22 | 00:10:00 | ||
Measure and Integration lec23 | 00:10:00 | ||
Measure and Integration lec24 | 00:10:00 | ||
Assessment | |||
Submit Your Assignment | 00:00:00 | ||
Certification | 00:00:00 |
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