Dyadic Cube [tex]C_{k,N} = X \in\ \mathbb{R}^{n} \frac{k_{i}}{2^{N}} \leq x_{i} < \frac{k_{i}+1}{2^{N}} for 1 \leq i \leq n[/tex](adsbygoogle = window.adsbygoogle || []).push({});

Where [tex]k = \pmatrix {

k_{1} \cr

k_{2} \cr

\vdots \cr

k_{i} \cr

} [/tex]

I understand that N is the level of the cubes, but what does k equal?

I'm having trouble visualizing this in my head.

[itex]A \subset \mathbb{R}^{n}[/itex]

[tex] M_{A}(f)= supp_{x \in A}f(x); m_{A}(f) = inf_{x \in A}f(x)[/tex] [tex] U_{N}(f) = \sum M_{c}(f) vol_{n}C [/tex] [tex] L_{N}(f) = \sum m_{c}(f) vol_{n}C [/tex]

I get the general idea, but I can't really see this in my head.

If you take the supp value of a function on a given cube, and multiply it by the volume of you cube, you get volume again??

I can't really get the image straight.

I get that this is just an extension of single variable, so it means that U must equal L which must equal I (integral).

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# Definition of Integral in Multiple Variables

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