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If we let J be in R^p so J=J1x....xJp the cartesian product of p cells in R. Then we define the content of J as c(J)=(b1-a1)....(bp-ap) so in like R it would be length area in R^2 etc. Then define content zero by Z in R^p has content zero if for each epsilon > 0 there exists a finite set J1,...,Jn of cells whose union contains Z and such that c(J1)+.....c(Jn) < epsilon. In an example we did we let the space in R^2 S=((x,y): |x|+|y|=1) and we proved that S has content zero by letting n natural number introducing squares with diagonals on the line in S. then S can be in enclosed in 4n squares each with content 1/n^2 so the total content is 4/n which can be made small so S has content zero. Where i'm confused is S is in R^2 so the cells of S are (-1,1) and (-1,1) so c(S)=(-1-1(-1-1)=4 but we showed S has content zero. This is confusing to me can anyone help clarify?

Thanks

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# Homework Help: Content math problem

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