Step function: Difference between revisions

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In mathematics, a [[function (mathematics)|function]] on the [[real number]]s is called a '''step function''' if it can be written as a [[finite set|finite]] [[linear combination]] of [[indicator function]]s of [[interval (mathematics)|interval]]s. Informally speaking, a step function is a [[piecewise]] [[constant function]] having only finitely many pieces.

[[Image:StepFunctionExample.png|thumb|right|250px|ExampleAn example of a step functionfunctions (the red graph). In this function, each constant subfunction with a function value ''α_i'' (''i'' = 0, 1, 2, ...) is defined by an interval ''A_i'' and intervals are distinguished by points ''x_j'' (''j'' = 1, 2, ...). This particular step function is [[Continuous function#Directional and semi-continuity|right-continuous]].]]

==Definition and first consequences==