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A blackboard-bold 1 with a set subscript, one inside and zero outside.
Also known as: Characteristic function of a set, Indicator variable, Bold one notation
The indicator function turns a set into a function: one for members, zero for everything else. It is what lets a probability be written as an expectation and a piecewise definition be written on one line, which is why it appears constantly in measure theory and statistics.
Denotes the function equal to 1 on a named set and 0 elsewhere.
Contexts: Mathematics
Makes the probability of an event equal to the expectation of its indicator, which is the identity most of measure-theoretic probability is built on.
Contexts: Mathematics
Is written as a bold or blackboard-bold 1, as a Greek chi, or as I; all three are current.
Contexts: Mathematics
A numeral one drawn with a doubled upright stroke, carrying a small set name below and to the right.