# Questions tagged [step-function]

A step function, also known as a simple function, is a finite sum of characteristic functions of bounded intervals. They are often used in measure theory to approximate integrable functions.

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### Examples of counterintuitive regulated functions (solution verification)

Questions I am looking for some counterexamples for properties that of functions that are commonly mistaken for being true in cases where they do not hold in general. The specific cases I am thinking ...
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### Is there a step function with an "in between value" that can be represented by a limit?

I would be interested if there is a function $f(x)$ with the property that when a limit on the parameters of the function is be performed you get a step function with an in between value. What I mean ...
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### Smoothing function to combine a polynomial and a constant

click to see the image I have below function: $y=0$ for $x<=0.12$ and $y=80((x/0.12)^8-1)$ for $x>0.12$ I need to smooth out the transition between these two functions. Can I find out the best ...