[continued from previous message]   
      
   > Here this usual notion of "removable discontinuity"   
   > is reflected in "negligeable collection" (or, negligible   
   > quantity).   
   >   
   > (Some tagged posts of T.Tao about measure and multiple   
   > recurrence:   
   >   
   > https://terrytao.wordpress.com/tag/lebesgue-measure/   
   > https://terrytao.wordpress.com/tag/multiple-recurrence/ )   
   >   
   >   
   >   
   > Then, there is room for dispute of "The Vitali covering   
   > theorem is not valid in infinite-dimensional settings",   
   > as where it's framed as about the Gaussian instead of   
   > as we discuss here other relevant measures, in the   
   > infinite-dimensional setting.  (And about a spiral-   
   > space-filling curve as finite- or infinite-dimensional.)   
   >   
   >   
   > There is much of this type of reasoning put to the   
   > van der Waerden theorem about arithmetic progressions   
   > much as an analog to Dirichlet/pigeonhole principle,   
   >   
   > https://en.wikipedia.org/wiki/Van_der_Waerden%27s_theorem   
   >   
   > except as a complement of how they disperse besides   
   > how they nest.   
   >   
   > "Van der Waerden's theorem is a theorem in the branch   
   > of mathematics called Ramsey theory."   
   >   
   >   
   > So, you can see that "re-Vitali-ization" is ongoing in   
   > mathematics writ large, and quite more accessibly these   
   > days then that as the dust arises of the construction,   
   > it all has to settle to the foundations again.  Then,   
   > looking to "re-Vitali-ize" measure as from some quite   
   > fundamental notions as the spiral-space-filling curve   
   > and unique properties of the equivalency function (in   
   > continuity, analysis, differential analysis, singularity   
   > theory, and probability theory) makes a neat course for   
   > then laying out what are building up as these quite   
   > immense structures in categorical algebra in descriptive   
   > set theory, as somewhat neatly primitive (and accordingly   
   > fundamental).   
   >   
      
   Wow, this is sounding kind of repetitive these days.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)