I have a few questions regarding the following piece from the MathML 3.0 spec (section 4.3.3.1 Uses of <domainofapplication>, <interval>, <condition>, <lowlimit> and <uplimit>)

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The general technique of using a condition element together with domainofapplication is quite powerful. For example, to extend the previous example to a multivariate domain, one may use an extra bound variable and a domain of application corresponding to a cartesian product:

<apply><int/>

<bvar><ci>x</ci></bvar>

<bvar><ci>y</ci></bvar>

<domainofapplication>

<set>

<bvar><ci>t</ci></bvar>

<bvar><ci>u</ci></bvar>

<condition>

<apply><and/>

<apply><leq/><cn>0</cn><ci>t</ci></apply>

<apply><leq/><ci>t</ci><cn>1</cn></apply>

<apply><leq/><cn>0</cn><ci>u</ci></apply>

<apply><leq/><ci>u</ci><cn>1</cn></apply>

</apply>

</condition>

<list><ci>t</ci><ci>u</ci></list>

</set>

</domainofapplication>

<apply><times/>

<apply><power/><ci>x</ci><cn>2</cn></apply>

<apply><power/><ci>y</ci><cn>3</cn></apply>

</apply>

</apply>

Note that the order of the inner and outer bound variables is significant.

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My questions:

- Does this exaple try to denote a double integral ? If yes, is
this the recommended way to do it ?

- Why is the <set> wrapper inside
<domainofapplication> necessary at all? Only because the
later happens to just take a single argument ?

In a set, however, I could put arbitrary elements. From the example I conclude that this use of <set> is very specific to the <domainofapplication> parent and hence requires a very specific element list. I could not find any specification about the required structure of this <set>.

- What purpose serves the last <set> element
<list>... ? We already have declared <bvar> t and u
(in that order) as set element 1 and 2. Why list them again ?
Does the final note of this section refer in any way to the use
of the <list> element ?

Thank you in advance,

Chris

<http://km-works.eu>