I have written an article titled “Defining the Most Generalized, Natural Extension of the Expected Value”. The keywords are #Prevalence, #Expected Value, #Uniform Measure, #Measure theory, #Uniform Cover, #Entropy, #Sample, #Linear, #Superlinear, #Choice Function, #Bernard's Paradox, #Pseudo-random

Note that I’m an undergrad (the paper I’ve written might not be rigorous and is far from perfect); however, I did the best I could.

Be sure to click this link:

https://www.researchgate.net/publication/368926381_Defining_The_Most_Generalized_Natural_Extension_of_The_Expected_Value_on_Measurable_Functions_Final_Version