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In the paper I'm writing I often encounter expressions like

$$\int dx_1 \int dx_2 \ldots \int dx_N \mathrm{<something>}.$$

In this form it is not that cumbersome, but things get worse when indices are not just successive integers, but elements of some given set. Is there some mathematical notation to write in the form like

$$\left( \prod_{n \in S} \int dx_n \right)\mathrm{<something>}$$

I am currently using $\prod$, like shown above, but I have to explain it in the beginning of the paper, and if there is some traditional notation for this, I would prefer to use it instead.

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  • $\begingroup$ Are you really looking at products? Or are you integrating functions of several variables? $\endgroup$ – user20266 Jun 1 '12 at 14:29
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    $\begingroup$ Let $x=(x_1,\ldots,x_N)$ and just write $\int dx\langle\text{something}\rangle$. $\endgroup$ – Samuel Jun 1 '12 at 14:37
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    $\begingroup$ you can just specify the domain of integration and leave the measure implicit, like so: first $X_S:=\prod_{i\in S} X_i$, then just write $\int_{X_S} <something>$ (assuming Fubini's theorem applies) $\endgroup$ – tomasz Jun 1 '12 at 16:24
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    $\begingroup$ In the notation $\displaystyle \frac{\partial^{|B| y}}{\prod_{j\in B}\partial x_j}$, the expression in the denominator is somewhat similar to at least part of what this question asks about. I used this in a paper. The set $B$ could be any of many different sets. $\endgroup$ – Michael Hardy Jun 1 '12 at 18:25
  • $\begingroup$ @Samuel : Your suggestion works only if the set $S$ referred to in the question is always $\{1,\ldots,N\}$. If the set $S$ can take any of many different values, it won't work. $\endgroup$ – Michael Hardy Jun 1 '12 at 18:27
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Just to have some closure: in the end I used the

$$\left( \prod_{n \in S} \int dx_n \right)\mathrm{<something>}$$

syntax with the explanation. It seems that there is no conventional notation for this.

@tomasz suggestion about declaring the integration area as $X_S := \prod_{i\in S} X_i$ is also viable. It is more understandable, but also more cumbersome if there are many different combinations appearing in formulas.

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