# Mathematical definitions of infill asymptotics

I am writing a paper that uses infill asymptotics and one of my reviewers has asked me to please provide a rigorous mathematical definition of what infill asymptotics is (i.e., with math symbols and notation).

I can't seem to find any in the literature and was hoping someone could either point me in the direction of some or provide me with a self-written definition.

If you are unfamiliar with infill asymptotics (also called fixed domain asymptotics) they are the following: Infill asymptotics are based on observations that get increasingly dense in some fixed and bounded region as their number increases.

Stated otherwise, infill asymptotics is where more data is collected by sampling more densely in a fixed domain.

I've already looked at Stein 1999 and Cressie 1993 but nothing "mathematically" rigorous there.