mean of a function

The idea is again that shapes are difficult entities to be dealt with directly, so manipulate them by means of a function.

This solution has its problems, though; it overloads the natural meaning of a function with an arbitrary convention.

In this context, Jensen's inequality places sharp estimates on the relationship between these two different notions of the mean of a function.

In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain.

In mathematics, the spherical mean of a function around a point is the average of all values of that function on a sphere of given radius centered at that point.

Using statistical notation, it is a well-known result that the mean of a function, f, of a random variable X is not necessarily the function of the mean of X.