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:
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“The consequences of our actions grab us by the scruff of our necks, quite indifferent to our claim that we have “gotten better” in the meantime.”
—Friedrich Nietzsche (1844–1900)