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comment Is a joint image measure of absolutely continuous image measures absolutely continuous?
Thanks for your answer. By the way, is there a standard name for the relationship between $h(\mu)$ with $f(\mu)$ and $g(\mu)$? It’s not a product measure of the two measures so what is it?
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accepted Is a joint image measure of absolutely continuous image measures absolutely continuous?
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asked Is a joint image measure of absolutely continuous image measures absolutely continuous?
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asked What scriptures describe Lakshmi’s serpent Kalyana?
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Sep
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reviewed Leave Open Are both pleasure experienced by wicked and the suffering by the afflicted person the result of their previous karma?
Sep
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comment How does the frequentist definition of probability work with non-measurable sets?
What does the notation $1_{x_i\in E}$ mean? Does it mean $1_E(x_i)$?
Sep
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Sep
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comment God's punishment
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Sep
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comment How does Hinduism differ from Western philosophy? What western beliefs are antithetical to Hindu beliefs?
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Sep
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comment How does the frequentist definition of probability work with non-measurable sets?
@pre-kidney Yes, I am assuming independence.
Sep
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comment How does the frequentist definition of probability work with non-measurable sets?
@pre-kidney I found this paper which may be relevant: arxiv.org/pdf/1208.3187.pdf
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comment How does the frequentist definition of probability work with non-measurable sets?
@RobertIsrael Well, regardless my question is about the first kind of scenario. I want to know what would happen if we fix a non-measurable set, and then take a randomly generated sequence.
Sep
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comment How does the frequentist definition of probability work with non-measurable sets?
@pre-kidney Yes, I am talking about a sequence of uniform random variables.
Sep
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comment What is the state of research on finding all Prime Knots with 17 Crossings?
Why isn’t this major news? Why hasn’t this result been published in journals?
Sep
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comment How does the frequentist definition of probability work with non-measurable sets?
Yeah, I’m familiar with Lebesgue inner measure and Lebesgue outer measure. It would certainly be convenient for the liminf to be the Lebesgue inner measure and the limsup to be the Lebesgue outer measure, but why do think that it’s the case?
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comment How does the frequentist definition of probability work with non-measurable sets?
@RobertIsrael Well, at least for a Lebesgue measurable set $E$, if we choose each $x_i$ using a uniform probability distribution on $0,1]$, I’m pretty sure that with probability one the limit will converge to the Lebesgue measure of $E$.
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