# Question on meaning of some symbols

by yungman
Tags: meaning, symbols
 P: 3,904 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.
 Sci Advisor P: 905 1) The supremum of {|f(x,y)|} where (x,y) ranges over the ball centered at 0 of radius delta: |(x,y)|=sqrt(x^2+y^2)=delta.
P: 3,904
 Quote by Landau 1) The supremum of {|f(x,y)|} where (x,y) ranges over the ball centered at 0 of radius delta: |(x,y)|=sqrt(x^2+y^2)=delta.
Thanks for you reply, so for

1) Is the upper bound of |f(x,y)| in the ball.

2) Is the whole 2D plane minus the circle center at 0 with radius $\delta$

P: 905
Question on meaning of some symbols

 Quote by yungman 1) Is the upper bound of |f(x,y)| in the ball.
The least upper bound, a.k.a. the supremum ;)
 2) Is the whole 2D plane minus the circle center at 0 with radius $\delta$
Yes.
Math
Emeritus
 2) Is the whole 2D plane minus the circle center at 0 with radius $\delta$