# Thread: Question on meaning of some symbols.

1. ## Question on meaning of some symbols.

I don't know the meaning of these:

1) $sup_{B_\delta}|f(x,y)|$

Where $B_\delta$ is the ball of radius $\delta$.

2) $\int \int _{R^2 \B_{\delta}} f(xy)dxdy$

I don't know what is $R^2 \B_{\delta}$

Please read my Latex because the symbol really don't show correctly.

2. ## I'll take a stab at it

Originally Posted by yungman
I don't know the meaning of these:

1) $sup_{B_\delta}|f(x,y)|$

Where $B_\delta$ is the ball of radius $\delta$.

2) $\int \int _{R^2 \B_{\delta}} f(xy)dxdy$

I don't know what is $R^2 \B_{\delta}$

Please read my Latex because the symbol really don't show correctly.
I believe the first symbol refers to an upper bound for the function and the second symbol refers to two-dimensional space.

3. Hello,
Originally Posted by yungman
I don't know the meaning of these:

1) $sup_{B_\delta}|f(x,y)|$

Where $B_\delta$ is the ball of radius $\delta$.

2) $\int \int _{R^2 \B_{\delta}} f(xy)dxdy$

I don't know what is $R^2 \B_{\delta}$

Please read my Latex because the symbol really don't show correctly.
Your latex is ok

Anyway, given that you know the center of the balls you're considering, the first would mean that we take the supremum of |f(x,y)| for x in $B_\delta$ (if y is fixed), or conversely. But this one is not very clear...

The second one means that you integrate in the area $B_\delta^2=B_\delta\times B_\delta$, that is to say for $x\in B_\delta$ and $y\in B_\delta$