The use of reverberation chambers often requires the assessment of quantities related to the average power density. This is usually estimated by collecting data from random realizations that are ideally independent, requiring a virtually large number of measurements to be carried out. In this paper, it is proven that an alternative estimator can be defined, requiring just one realization. The estimator is based on a space-averaging approach, and it is shown to be unbiased and asymptotically convergent in probability to the classical ensemble averaging currently used. In other words, power density is shown to be asymptotically ergodic in space. Applications range from faster measurements in reverberation chambers to a solution to the problem of insufficiently large populations of independent samples.