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|An online course on measure theory, lebesgue integration and probability, with tutorials (in PDF format) designed as a set of simple exercises, leading gradually to the establishment of deeper results. Proved theorems, as well as clear definitions, are spelt out for future reference. The tutorials do not contain any formal proofs, but offer students the means of proving everything themselves. Specific tutorials are provided for: Dynkin systems; Caratheodory's extension; Stieltjes-Lebesgue measure; Measurability; Lebesgue integration; Product spaces; Fubini theorem; Jensen's inequality; Lebesgue functional spaces; Linear functionals in L2; Complex measures; Radon-Nikodym theorem; Regularity of measures; Maps of finite variations; Stieltjes integration; Differentiation; Image measure; Jacobean formula; Fourier transform; and Gaussian measures.|
|Resource Types:||Courses, Tutorials|
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