In measure theory, a simple function is a function that is a finite linear combination
of characteristic functions, where the are real coefficients and every is a measurable set with respect to a fixed measure space.
If the measure space is and each is an interval, then the function is called a step function. Thus, every step function is a simple function.
Simple functions are used in analysis to interpolate between characteristic functions and measurable functions. In other words, characteristic functions are easy to integrate:
while simple functions are not much harder to integrate:
To integrate a measurable function, one approximates it from below by simple functions. Thus, simple functions can be used to define the Lebesgue integral over a subset of the measure space.
|Date of creation||2013-03-22 12:21:16|
|Last modified on||2013-03-22 12:21:16|
|Last modified by||mps (409)|