# Is there an abbreviation for “almost all $x\in X$”?

Is there an abbreviation for "almost all $x\in X$?

I have "$\forall a.e. x\in X$" in my mind, but i see nobody uses this..

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Although the standard is "a.e", I've heard that some people used to use "p.p.", which stands for the French "presque partout" - "almost everywhere". –  Isaac Solomon Jan 15 at 5:03
I would find $\forall a.e.$ confusing as $\forall$ by itself denotes "for all." Hence $\forall a.e.$ would seem to denote "for all almost every." I think a.e. is a good abbreviation, and artificially defining another abbreviation seems not worth the trouble. Writing "For almost every" is painless and avoids abbreviations (and hence any confusion). –  JavaMan Jan 15 at 5:09
Not attempting to answer the question, but commenting on-topic: I've always liked the visual information quickly conveyed by $\forall$ (something the phrase "for all" just can't do), so in my own notes I've started using $\stackrel{a.}{\forall}$ –  Dahn Jahn Jan 15 at 9:08
I myself have used: "for a.a. $x\in X$" or "for $\mu$-a.a. $x\in X$" to emphasize which measure it is with respect to. –  Stefan Hansen Jan 15 at 9:18

You can use $\mu$-a.e $x\in X$ (because depends on measure).

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I write this as a.e. $[\mu]$. –  mrf Jan 15 at 9:02
And probabilists write $\mu$-a.s. (almost surely). –  Michael Greinecker Jan 15 at 9:31

It's common to see things like if $\int_a^b |f|dx=0$ then for a.e. $x \in [a,b]$ we have $f(x)=0$. I've never seen the notation $\forall a.e. x \in X$ personally. Of course it's also not too many characters to write out for almost every $x \in X$.

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