[patrick5415]

I disagree that statisticians should adjust their definitions to fit common usage.

I can put any probably on anything I want. That doesn’t imply those numbers mean anything usefu or that what I’m doing is backed by any established theory.

[kgwgk]

There are established theories of probability that have nothing to do with ergodicity. See for example:

Laplace - Théorie analytique des probabilités - 1812

Keynes - A Treatise on Probability - 1921

Jeffreys - Theory of Probability - 1939

Savage - The Foundations of Statistics - 1954

de Finetti - Teoria delle Probabilità - 1970