(Why) are you not happy with Velenik’s answer or “a probabilistic theory (Ω,F,P) tells us that if we look at an event A∈F and perform the same experiment N→∞ times, then the fraction of experiments where A happened approaches P(A) in a LLN-like manner”? Is there something special about physical phenomena as opposed to observables?
>[0,1] can be written as the union of a meager set and a set of null measure. This result forces us to make a choice as to which class of sets we will neglect, or otherwise we will end up neglecting the whole space [0,1]!
Either neither of these sets are measurable or this meagre set has measure 1. Either way, it seems obvious what to neglect.
(Why) are you not happy with Velenik’s answer or “a probabilistic theory (Ω,F,P) tells us that if we look at an event A∈F and perform the same experiment N→∞ times, then the fraction of experiments where A happened approaches P(A) in a LLN-like manner”? Is there something special about physical phenomena as opposed to observables?
>[0,1] can be written as the union of a meager set and a set of null measure. This result forces us to make a choice as to which class of sets we will neglect, or otherwise we will end up neglecting the whole space [0,1]!
Either neither of these sets are measurable or this meagre set has measure 1. Either way, it seems obvious what to neglect.