Of course one can write . How about ellipses? Or a square? A rectangle?

]]>Thanks a lot for your notes. I think that there might be a typo in Exercise 42. The formula in the hint should read x_j (f*g)= (x_j f)*g+f*(x_j g). This is the only way that I can get to show that the left hand side converges uniformly to x_j f, when g=g_r, as r tends to zero.

*[Corrected, thanks – T.]*

where $S\subset \mathbf{R}^n$ is the unit sphere centered

Reading around the context of the notes one can see that

It seems that should be a ball in .

How can one make sense of the canonical measure , which is originally defined for the sphere , “evaluating” on the ball in , and thus make sense of the second inequality above?

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