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In probability theory, a conditional event algebra (CEA) is an alternative to a standard, Boolean algebra of possible events (a set of possible events related to one another by the familiar operations and, or, and not) that contains not just ordinary events but also conditional events that have the form "if A, then B".
Events A and B can be assumed to be independent i.e. knowledge that A is late has minimal to no change on the probability that B will be late. However, if a third event is introduced, person A and person B live in the same neighborhood, the two events are now considered not conditionally independent.
In mathematics, a dependence relation is a binary relation which generalizes the relation of linear dependence.. Let be a set.A (binary) relation between an element of and a subset of is called a dependence relation, written , if it satisfies the following properties:
The notation ba is a mnemonic for bounded additive and ca is short for countably additive. If X is a topological space , and Σ is the sigma-algebra of Borel sets in X , then r c a ( X ) {\displaystyle rca(X)} is the subspace of c a ( Σ ) {\displaystyle ca(\Sigma )} consisting of all regular Borel measures on X .
In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) [5] and providing an output (which may also be a number). [5] A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. [6]
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
The domain of a structure is an arbitrary set; it is also called the underlying set of the structure, its carrier (especially in universal algebra), its universe (especially in model theory, cf. universe), or its domain of discourse. In classical first-order logic, the definition of a structure prohibits the empty domain. [citation needed] [5]
The language of mathematics has a wide vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject. Jargon often appears in lectures, and sometimes in print, as informal shorthand for rigorous arguments or precise ideas. Much ...
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