I have the following formula in the beginning of the basics of probability theory. The notes only say that we define this function. What does this function serve to ? What does it tell ? What is 1 and subscript the range? I have really hard time understanding the notation and meanings. Any help is appreciated.
2026-03-31 18:34:23.1774982063
Dyadic Function
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I saw that function used to prove that every positive measurable function is the limit of a sequence of positive simple functions by setting $f_n(x)=d_n(f(x))$ for any positive measurable function $f$. I'm not sure if it's useful for other things.