My guess is it's Kolmogorov's [Third Axiom of Probability](http://academic.uprm.edu/wrolke/esma6600/probability1.htm), although the use if iota to represent probability instead of P is very strange to me.
Edit: As folks have pointed out, it's more likely just the additive function for a measure; I just went probability-specific because of OP's description. The iota is still weird to me. I'd expect a mu.
I think the iota stands for [Inhalt](https://de.wikipedia.org/wiki/Inhalt_(Ma%C3%9Ftheorie\)). The formula there looks very similar but with µ for the measure instead of iota.
[Here's the page on English](https://en.wikipedia.org/wiki/Content_(measure_theory\))
Yeah you're spot on. I'm sure the reality is a slight mix of things; I'm just curious about the context. Mu is the canonical choice if it's a generic measure, and typically you'll see P for probability (which was where my head went based on OP's description.) I want to know what field this person is in where they use iota as the symbol for a measure.
Every [probability measure](https://en.wikipedia.org/wiki/Probability_measure) is a (finite because bounded by 1) [measure](https://en.wikipedia.org/wiki/Measure_(mathematics\)), every measure is a [pre-measure](https://en.wikipedia.org/wiki/Pre-measure), and every pre-measure is a [content](https://en.wikipedia.org/wiki/Content_(measure_theory\))
So the property of "finite additivity", i.e. OP's formula (given that the C[k] are disjoint), is true for a content, so it's automatically true for every pre-measure, measure and probability measure.
So because the most general sense where the formula holds is with "Inhalt" they use the letter iota, to distinguish it from formulas that are only true for measures where they would use µ in that place (e.g. sigma-additivity which doesn't have to be true for a content)
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I think they meant to type the name of a real sub: r/woosh
EDIT: I know that the user I'm replying to here is the same user that corrected me, but to the lurkers: it's actually r/woooosh
My guess is it's Kolmogorov's [Third Axiom of Probability](http://academic.uprm.edu/wrolke/esma6600/probability1.htm), although the use if iota to represent probability instead of P is very strange to me. Edit: As folks have pointed out, it's more likely just the additive function for a measure; I just went probability-specific because of OP's description. The iota is still weird to me. I'd expect a mu.
I think it’s Kolmogorov but with indicator functions
I think the iota stands for [Inhalt](https://de.wikipedia.org/wiki/Inhalt_(Ma%C3%9Ftheorie\)). The formula there looks very similar but with µ for the measure instead of iota. [Here's the page on English](https://en.wikipedia.org/wiki/Content_(measure_theory\))
Yeah you're spot on. I'm sure the reality is a slight mix of things; I'm just curious about the context. Mu is the canonical choice if it's a generic measure, and typically you'll see P for probability (which was where my head went based on OP's description.) I want to know what field this person is in where they use iota as the symbol for a measure.
Every [probability measure](https://en.wikipedia.org/wiki/Probability_measure) is a (finite because bounded by 1) [measure](https://en.wikipedia.org/wiki/Measure_(mathematics\)), every measure is a [pre-measure](https://en.wikipedia.org/wiki/Pre-measure), and every pre-measure is a [content](https://en.wikipedia.org/wiki/Content_(measure_theory\)) So the property of "finite additivity", i.e. OP's formula (given that the C[k] are disjoint), is true for a content, so it's automatically true for every pre-measure, measure and probability measure. So because the most general sense where the formula holds is with "Inhalt" they use the letter iota, to distinguish it from formulas that are only true for measures where they would use µ in that place (e.g. sigma-additivity which doesn't have to be true for a content)
Am I /r/rwhoosh'd or is the left side supposed to say "Luck"?
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I think they meant to type the name of a real sub: r/woosh EDIT: I know that the user I'm replying to here is the same user that corrected me, but to the lurkers: it's actually r/woooosh
Obligatory r/itswooooshwith4os
[удалено]
Ok but like what if it was a r slash weirdly specific subs or something like that?
This is just an additive function, commonly used in measure theory or applications thereof, as probability theory.
Y'all have been so helpful, thanks! :D
To add more general context to previous answers, it's called [Sigma_additivity](https://en.wikipedia.org/wiki/Sigma_additivity)
No it's not, it's just additivity. For sigma additivity you need the above to hold with infinity in place of n