ABSTRACT
We let (µi)i≥1 be a sequence of probability measures on a given measurable state space (E, E). During the further development of this chapter, we fix an integer N ≥ 1. To clarify the presentation, with a slight abuse of notation denoted respectively, by
m(X) = 1
N
δXi and µ = 1
N
µi
the N -empirical measure is associated with a collection of independent random variables X = (X i)i≥1, with respective distributions (µi)i≥1, and the N -averaged measure is associated with the sequence of measures (µi)i≥1.
