In the table below, 1 is the indicator function.

It is just the indicator function for the different knot spans.

In many cases, such as order theory, the inverse of the indicator function may be defined.

The indicator function of a closed set is upper semicontinuous.

The indicator function is also known as the characteristic function.

The indicator function, another specific case, has set membership as its condition:

In this sense, the term predicate has the meaning of a mathematical indicator function.

Here is the indicator function of the positive half-line.

If is the indicator function for a cone .

In this formula is I the indicator function.

Of course, can also be interpreted as the mean of the indicator function :

Here the indicator function emphasizes that the penalty is exercised only when ruin occurs.

It may be described as the "indicator function of 1" within the set of positive integers.

If there are constraint conditions, these can be built in to the function by letting where is the indicator function.

As suggested by the previous example, the indicator function is a useful notational device in combinatorics.

A particular indicator function, which is very well known, is the Heaviside step function.

For a digital option payoff is , where is the indicator function.

In this case H is the indicator function of a closed semi-infinite interval:

(This is the Cesaro limit of the indicator functions.

This can be equivalently written as where is the lower -quantile and is the indicator function.

In writing out the likelihood function, we first define an indicator function where:

A conditional risk measure is said to be regular if for any and then where is the indicator function on .

The associated indicator function is a Bernoulli process with a success probability that depends on the magnitude of the extreme event.

In other words, is simply the number whose binary expansion corresponds to the indicator function of the set of prime numbers.

Likewise, it is at most as innocent as set theory, because any set can be identified with its indicator function.