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This course continues the content covered in 18.100 Analysis I. Roughly half of the subject is devoted to the theory of the Lebesgue integral with applications to probability, and the other half to Fourier series and Fourier integrals. Topics covered in this course such as coin Tossing, Law of Large Numbers, Rademacher Functions,     Measure Theory, Random Model, Boolean Rings, Lebesgue Spaces, Measurable Functions and Lebesgue Integral.


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.


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Course Credit: MIT

Course Curriculum

lec1 Coin Tossing, Law of Large Numbers, Rademacher Functions 00:20:00
lec2 Measure Theory, Random Models 00:15:00
lec3 Lebesgue Spaces, Inner Products 00:25:00
lec4 Hilbert Space, Midterm Review 00:30:00
lec5 Fourier Series and their Convergence1 00:30:00
lec6 Fourier Series and their Convergence 2 00:20:00
lec7 Applications of Fourier Series 00:30:00
lec8 Fourier Integrals 00:20:00
lec9 Fourier Integrals of Measures, Central Limit Theorem 00:30:00
lec10 Brownian Motion 00:35:00
Submit Your Assignment 00:00:00
Certification 00:00:00

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