Timeline for Singular Radon probabilities on $[0,1]^d$. Is conditioning on $x_i = \alpha$ well-defined?
Current License: CC BY-SA 4.0
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| Sep 27, 2019 at 1:46 | comment | added | R W | Sure - still thank you for making clear this distinction - as otherwise your answer could be misinterpreted. | |
| Sep 26, 2019 at 21:39 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 26, 2019 at 21:21 | comment | added | Iosif Pinelis | @RW : You are of course right, it would be incorrect to say "the conditional measures are well-defined for all $\alpha\in[0,1]$. Of course, I did not say anything like that. Rather, I said "you can let $\mathbf P_\pi [\cdot \mid x_i=\alpha]:=\nu_i(\alpha,\cdot)$ for all $\alpha\in[0,1]$." I also said "a regular conditional probability distribution", not "the regular conditional probability distribution". To make it quite clear, I have now also added a remark about the nonuniqueness of a regular conditional probability distribution. | |
| Sep 26, 2019 at 21:17 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 26, 2019 at 18:06 | comment | added | R W | It is completely misleading to claim that the conditional measures are well-defined for all $\alpha\in[0,1]$. | |
| Sep 26, 2019 at 17:05 | vote | accept | Vojtěch Kovařík | ||
| Sep 26, 2019 at 16:44 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 26, 2019 at 15:49 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |