🚀 go-pugleaf

In article <17dh96INN35s@function.mps.ohio-state.edu> edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:

   (I seem to remember seeing this, but can't remember for sure.)

   Let S be a metric space.  Write B(x,r) for the open ball with center
   x and radius r.  Let mu be a finite Borel measure on S.  For fixed
   r>0, does it follow that the function

      x --->  mu(B(x,r))

   (from S to R) is a Borel function of x ?

   Assume, if necessary, that S is separable.
   -- 
     Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
     Department of Mathematics      Bitnet:    EDGAR@OHSTPY
     The Ohio State University      telephone: 614-292-0395 (Office)
     Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)

*****
I do think this function is lower semicontinuous! Thus always
measurable!

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