Categories
Ask Mathematics

Is there a difference between those two notions of “almost everywhere”?

Assume we have two functions $f$ and $g$ on, say, the interval $[0,1]$. Let’s say that $g$ is continuous, i.e. the pointwise evaluation $g(x)$ makes sense. $f$, on the other hand, is only $L^1([0,1])$ and thus not defined pointwise. Is there a difference between saying a) $f = g$ a.e. on [0,1]$ and b) There […]

Categories
Ask Mathematics

Is there a difference between those two notions of “almost everywhere”?

Assume we have two functions $f$ and $g$ on, say, the interval $[0,1]$. Let’s say that $g$ is continuous, i.e. the pointwise evaluation $g(x)$ makes sense. $f$, on the other hand, is only $L^1([0,1])$ and thus not defined pointwise. Is there a difference between saying a) $f = g$ a.e. on [0,1]$ and b) There […]