منابع مشابه
Probability Theory
4 The Lebesgue integral and expectation 14 4.1 The Lebesgue integral and convergence theorems . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2 Probability measures and modes of convergence . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Uniform integrability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.4 Jensen’s inequality . . . . . ...
متن کاملProbability Theory
Probability theory comprises mathematically based theories and methods for investigating random phenomena. Formally, random phenomena occur in connection with random experiments. A random experiment is characterized by two properties: 1. Repetitions of the experiment, even if carried out under identical conditions, generally have different outcomes. 2. The possible outcomes of the experiment ar...
متن کاملProbability Theory
A set is defined as collection of objects, or elements. Familiar examples are the set of greek letters, f ̨; ˇ; !; : : : ; !g, the set of binary values, B D f0; 1g, and the set of integers Z D f: : : ;!1; 0; 1; : : :g, the set of positive integers (or natural numbers) N D ZC D f1; 2; 3; : : :g, the set of negative integers Z! D f!1;!2;!3; : : :g, and the set of nonpositive integers Z" D f0; 1; 2...
متن کاملProbability Theory
This paper introduces some elementary notions in Measure-Theoretic Probability Theory. Several probabalistic notions of the convergence of a sequence of random variables are discussed. The theory is then used to prove the Law of Large Numbers. Finally, the notions of conditional expectation and conditional probability are introduced. 1 Heuristic Introduction Probability theory is concerned with...
متن کاملAn Algebraic Characterization of the Halting Probability
Using 1947 work of Post showing that the word problem for semigroups is unsolvable, we explicitly exhibit an algebraic characterization of the bits of the halting probability Ω. Our proof closely follows a 1978 formulation of Post’s work by M. Davis. The proof is selfcontained and not very complicated.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1990
ISSN: 0001-8708
DOI: 10.1016/0001-8708(90)90050-w