Finally, in group 4, we have again constructed an ensemble average, but there are no significant features.

Thus there are fluctuations in the field about the zero ensemble average.

The averaging need not be taken over time; an ensemble average can also be taken, with equivalent results.

Also, it is now possible to perform ensemble averages directly.

To make up for this assumption, another equation of ensemble average is used:

The power spectrum can then be defined via the ensemble average of the Fourier components:

The theorem allows the time average of a conforming process to equal the ensemble average.

We can formally count these particles as , with the ensemble average, yielding:

In statistics, the term describes a random process for which the time average of one sequence of events is the same as the ensemble average.

If both ensemble average and time average are same then it is ergodic.