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→Properties: minor refinement of the 'discrete random variables' example |
→Definition and first consequences: noted some common variations in the definition (I will add more references that are not from the internet) |
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can be written as
:<math>f = 0\chi_{(-\infty, -5)} +4 \chi_{[-5, 0]} +7 \chi_{(0, 1)} + 3 \chi_{[1, 6)}+0\chi_{[6, \infty)}.</math>
===Variations in the definition===
Sometimes, the intervals are required to be right-open<ref>http://mathworld.wolfram.com/StepFunction.html</ref> or allowed to be singleton <ref>http://mathonline.wikidot.com/step-functions</ref>. The condition that the collection of intervals must be finite is often dropped, especially in school mathematics<ref>https://www.mathwords.com/s/step_function.htm</ref><ref>https://study.com/academy/lesson/step-function-definition-equation-examples.html</ref><ref>https://www.varsitytutors.com/hotmath/hotmath_help/topics/step-function</ref>, though it must still be locally finite, resulting in the definition of piecewise constant functions.
==Examples==
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