I don't understand how a distribution can converge to another distribution if they're not defined on the same probability space or same experiment.
Could someone maybe provide some trivial examples and/or intuition so I could grasp this?
2026-03-25 06:05:39.1774418739
Intuition behind distributions not being defined on the same sample space but one is convergent to the other
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Let's take a simpler case than convergence in distribution. It's possible for two random variables to have the same distribution without being defined on the same space.
For example, suppose I take a random person and measure their height. This gives me a real valued random variable. The probability space is the set of all people. I could also take a random ball bearing from a ball bearing factory and measure its density. The space is the set of all ball bearings in the factory, and the variable is again real value. Now, it may be the case that, by coincidence, these two real random variables happen to have the same distribution. The fact that they're defined on different spaces doesn't matter, what matters is that they're both random real numbers.