Definition and First Consequences
A function is called a step function if it can be written as
- for all real numbers
where are real numbers, are intervals, and is the indicator function of :
In this definition, the intervals can be assumed to have the following two properties:
- The intervals are disjoint, for
- The union of the intervals is the entire real line,
Indeed, if that is not the case to start with, a different set of intervals can be picked for which these assumptions hold. For example, the step function
can be written as
Read more about this topic: Step Function
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