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
Famous quotes containing the words definition and/or consequences:
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“There are more consequences to a shipwreck than the underwriters notice.”
—Henry David Thoreau (1817–1862)