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<?xml version="1.0"?>
<api>
  <query-continue>
    <pageswithprop pwpcontinue="1119" />
  </query-continue>
  <query>
    <pageswithprop>
      <page pageid="439" ns="0" title="Pre-image sigma-algebra" value="Pre-image [ilmath]\sigma[/ilmath]-algebra" />
      <page pageid="461" ns="0" title="D-system" value="d-system" />
      <page pageid="462" ns="0" title="A collection of subsets is a sigma-algebra iff it is a Dynkin system and closed under finite intersections" value="A collection of subsets is a [ilmath]\sigma[/ilmath]-algebra [ilmath]\iff[/ilmath] it is both a [ilmath]p[/ilmath]-system and a [ilmath]d[/ilmath]-system" />
      <page pageid="465" ns="0" title="A map from two sigma-algebras, A and B, is measurable if and only if for some generator of B (call it G) we have the inverse image of S is in A for every S in G" value="A map, [ilmath]f:(A,\mathcal{A})\rightarrow(F,\mathcal{F})[/ilmath], is [ilmath]\mathcal{A}/\mathcal{F} [/ilmath] measurable &lt;i&gt;if and only if&lt;/i&gt; for some generator [ilmath]\mathcal{F}_0[/ilmath] of [ilmath]\mathcal{F} [/ilmath] we have [ilmath]\forall S\in\mathcal{F}_0[f^{-1}(S)\in\mathcal{A}][/ilmath]" />
      <page pageid="469" ns="0" title="Min/max" value="min/max" />
      <page pageid="507" ns="0" title="P-system" value="[ilmath]p[/ilmath]-system" />
      <page pageid="640" ns="0" title="R+ (notation)" value="[ilmath]\mathbb{R}_+[/ilmath] (notation)" />
      <page pageid="754" ns="0" title="Exists functor" value="[ilmath]\exists[/ilmath]-functor" />
      <page pageid="932" ns="0" title="Hereditary sigma-ring" value="Hereditary [ilmath]\sigma[/ilmath]-ring" />
      <page pageid="1055" ns="0" title="Given a topological manifold of dimension 2 or more and points p1, p2 and q where q is neither p1 nor p2 then a path from p1 to p2 is path-homotopic to a path that doesn&#039;t go through q" value="Given a topological manifold of dimension 2 or more and points [ilmath]p_1[/ilmath], [ilmath]p_1[/ilmath] and [ilmath]q[/ilmath] where [ilmath]q[/ilmath] is neither [ilmath]p_1[/ilmath] nor [ilmath]p_2[/ilmath] then a path from [ilmath]p_1[/ilmath] to [ilmath]p_2[/ilmath] is path-homotopic to a path that doesn&#039;t go through [ilmath]q[/ilmath]" />
    </pageswithprop>
  </query>
</api>