# Stuart

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# 207 Actions

 Nov9 awarded Yearling Jul2 awarded Curious Jul2 awarded Inquisitive Jan3 awarded Popular Question Nov9 awarded Yearling Jun11 asked Continuity of $x^2$ over $\overline{\mathbb{R}}$ Jun4 comment Correspondence between modes of convergence and metrics Yes, thanks, I know what you mean. I'm looking for general case then. Jun4 comment Correspondence between modes of convergence and metrics Just a general question, not homework, I'd like to see any relevant answers. Jun4 asked Correspondence between modes of convergence and metrics Jun3 accepted Uniqueness of convergence in measure Jun3 asked Uniqueness of convergence in measure Jun2 accepted $f=g\; ; \;\bar{\mu}$-a.e. vs $\mu$-a.e. Jun2 accepted Default way of defining measure on subset of measure space May31 comment $f=g\; ; \;\bar{\mu}$-a.e. vs $\mu$-a.e. You're saying that if we use another definition, then the statement is false. My question is whether this alternate definition is ever used in practice? That is, could you point to an theorem where this alternate definition is used, but my given definition wouldn't work? May31 asked Default way of defining measure on subset of measure space May31 comment $f=g\; ; \;\bar{\mu}$-a.e. vs $\mu$-a.e. Could you give an example of where it's needed to use the $\mu(f \ne g) = 0$ definition? Obviously it's not useful for integration theory (what I'm studying), but I'd be interested in knowing where it's useful. May31 revised $f=g\; ; \;\bar{\mu}$-a.e. vs $\mu$-a.e. added 193 characters in body May31 asked $f=g\; ; \;\bar{\mu}$-a.e. vs $\mu$-a.e. May30 accepted Find a measurable function such that $f(x)\le \alpha$ for $x\in E_\alpha$ May30 accepted Metric assuming the value infinity