- #1

gotjrgkr

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## Homework Statement

While studying a book "analysis on manifolds" by munkres, I see a definition of measure zero. That is,

Let A be a subset of R[itex]^{n}[/itex]. We say A has measure zero in R[itex]^{n}[/itex] if for every ε>0, there is a covering Q[itex]_{1}[/itex],Q[itex]_{2}[/itex],... of A by countably many rectangles such that [itex]\sum[/itex][itex]_{i=1}[/itex][itex]^{\infty}[/itex]v(Q[itex]_{i}[/itex])<ε.

But, in this text, there's no remark about the countable set. I mean, it seems to me that countable set is not defined.

Could you tell me what the "countably many" mean in the above definition??