introduction-probability.pdf

# Jensens inequality 66 law of a random variable 39

• pauloffei201440
• 91

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Jensen’s inequality, 66 law of a random variable, 39 Lebesgue integrable, 47 Lebesgue measure, 26, 27 Lebesgue’s Theorem, 55 lemma of Borel-Cantelli, 20 lemma of Fatou, 18 lemma of Fatou for random variables, 54 measurable map, 38 measurable space, 10 measurable step-function, 35 measure, 14 measure space, 14 Minkowski’s inequality, 68 88

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INDEX 89 moments, absolute moments, 59 monotone class theorem, 60 monotone convergence, 53 open set, 12 Poisson distribution, 25 Poisson’s Theorem, 29 probability measure, 14 probability space, 14 product of probability spaces, 23 random variable, 36 realization of independent random variables, 44 step-function, 35 strong law of large numbers, 74 uniform distribution, 26, 27 variance, 49 vector space, 59 weak law of large numbers, 73
90 INDEX

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Bibliography [1] H. Bauer. Probability theory . Walter de Gruyter, 1996. [2] H. Bauer. Measure and integration theory . Walter de Gruyter, 2001. [3] P. Billingsley. Probability and Measure . Wiley, 1995. [4] A.N. Shiryaev. Probability . Springer, 1996. [5] D. Williams. Probability with martingales. Cambridge University Press, 1991. 91
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• Spring '17
• Probability, Probability theory, Probability space, measure, lim P, Probability Spaces

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