MTL270: Measure Integral and Probability

3 Credits (3-0-0)

Overlaps with: MTL510

Measurable spaces, measurable sets, measurable functions, measure, outer measures and generation of measure, Lebesgue integration, basic integration theorem, comparison of Lebesgue and Riemann integrals, various modes of convergence of measurable functions, signed measure, Hahn and Jordan decomposition theorems, the Radon-Nikodym theorem, product measures and Fubini’s theorem, probability measures and spaces, independent events, conditional probability, theorem of total probability, random variables, distribution and distribution function of a random variable, independent random variable, expectation, convergence in distribution of a sequence of random variables, weak and strong laws of large numbers, Kolmogorov’s zero-one law, the central limit theorem, identically distributed summands, the Linderberg and Lyapounov theorems.