Hello www-math@w3.org,
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:
  1. Does this exaple try to denote a double integral ? If yes, is this the recommended way to do it ?
  2. 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>.
  3. 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 ?
Any comments or expalantions would be greatly appreciated.

Thank you in advance,
Chris

<http://km-works.eu>