Probability Spaces and Random Variables
1989
Let Ω be an arbitrary non-empty set and P(Ω) be the aggregate of all its subsets. The class A ⊂ P(Ω) is said to be a Boolean algebra (an algebra), if: (a) Ω ∈ A; (b) A is closed with respect to the operations of union, intersection and complementation; i.e., from A, B ∈ A it follows that A ∪ B ∈ A, AB ∈ A and Ā ∈ A.
Keywords:
- Multivariate random variable
- Combinatorics
- Regular conditional probability
- Boolean algebra
- Conditional probability table
- Random element
- Probability distribution
- Algebra of random variables
- Topology
- Random variable
- Mathematics
- Convergence of random variables
- Discrete mathematics
- Convolution of probability distributions
- Sum of normally distributed random variables
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