I have a question about normed space and integrable.
If $f$ is in $L_\infty$, $g$, which is $g \le f$, can be absolutely integrable ($g$ is in $L_1$)?
And how can I prove it?
I have a question about normed space and integrable.
If $f$ is in $L_\infty$, $g$, which is $g \le f$, can be absolutely integrable ($g$ is in $L_1$)?
And how can I prove it?
Yes, it can: $f(x)=1$ and $g(x)=0$, $x \in \mathbb{R}$.
But it need not be: $f(x)=1$, $g(x)=1/2$, $x \in \mathbb{R}$.