Prove that all balls in R^n are Jordan regions.
For rectangles it is easy enough, but I can't seem to find a way of proving it for balls. Thanks for the help in advance!
Yes they're the same, and you actually have the definition that's useful in this case!
Remember that is countable and ennumerate it by . Given take cover the sphere (boundary of the ball) with sets of the form then certainly covers your sphere and since this last one is compact it can be covered by a finite number of these, say (after possibly renaming them) then so the volume of the sphere is bounded by an arbitrarily small number.