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## Main Question or Discussion Point

0. Introduction
As for the reference material I have used the text Special Functions by Askey, Andrews, and Roy which covers much of the theorems here outlined. Another reference text, I cite Theory and Applications of Infinite Series by Knopp. As for original content I only have hope that the method of using the sets
$$C_N^n: = \left\{ {\vec x \in {\mathbb{R}^n}|{x_i} \ge 0\forall i,\sum\limits_{k = 1}^n {x_k^{2N}} < n – 1} \right\}$$
and Dirichlet integrals to evaluate the integrals
$$\mathop {\lim }\limits_{N \to \infty } \int\limits_{C_N^n} {f\left( {\vec x} \right)d\mu } = \int\limits_{{{\left[ {0,1} \right]}^n}} {f\left( {\vec x} \right)d\mu }$$
might be original material as I have never seen it my reading though there is nothing new under...

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mathman
Do you have a specific question? $\lim_{N\to \infty} C_N^n=[0,1)$ is straightforward.

Homework Helper
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Yes, it is, I had used that particular definition of $C_N^n$ with the $\leq n-1$ (opposed to $\leq n$) to accommodate and singular point of an a few integrands in section 4, whereas the latter would converge to $\left[ 0,1\right]$. These two definitions cover all of the integrals in the text.

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I updated the Insight to include more exercises in sections 4 and 5 and added a few answers to section 1 at the end.