 Next we have the space average \(\bar{f}\). Let us again start with a colloquial example: the average height of the students in a particular school. This is easily calculated: just take each student’s height, add up all the numbers, and divide the result by the number of students. Technically speaking this is a space average. In the example the students in the school correspond to the points in \(X\); and the fact that we count each students once (we don’t, for instance, take John’s height into account twice and omit Jim’s) corresponds to the choice of a measure that gives equal ‘weight’ to each point in \(X\). The transformation \(T\) has no pendant in our example, and this is deliberate: space averages have nothing to do with the dynamics of the system (that’s what sets them off from time averages). The general mathematical definition of the space average is as follows: