Thread: Question on meaning of some symbols.

1. Question on meaning of some symbols.

I don't know the meaning of these:

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

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

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

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

2. I'll take a stab at it

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

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

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

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

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

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

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

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

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

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 $\displaystyle B_\delta$ (if y is fixed), or conversely. But this one is not very clear...
The second one means that you integrate in the area $\displaystyle B_\delta^2=B_\delta\times B_\delta$, that is to say for $\displaystyle x\in B_\delta$ and $\displaystyle y\in B_\delta$