1
$\begingroup$

Please help me understand how the below definition is equivalent to the standard definition of regularity which says that a measure is regular if for which every measurable set can be approximated from above by an open measurable set and from below by a compact measurable set. http://en.wikipedia.org/wiki/Regular_measure

Second def. "μ is regular whenever A is in the domain of definition of Borel algebra and δ>0, there are closed and open sets C and U. such that C⊂A⊂U and |μ|(U\ C)<ϵ."

Improve this question
$\endgroup$
4
  • $\begingroup$ Not all definitions of regular measures are equivalent, so you should be more explicit with what the "standard definition" is. Also, this is not really research mathematics, so you might want to ask this where such questions are appropriat, such as math.stackexchange.com $\endgroup$
    – Michael Greinecker
    Commented Apr 21, 2013 at 11:31
  • $\begingroup$ Thanks Michale, I have added the definition which I was referring to.. $\endgroup$
    – user28112
    Commented Apr 21, 2013 at 11:42
  • $\begingroup$ They are not equivalent. $\endgroup$
    – Michael Greinecker
    Commented Apr 21, 2013 at 12:07
  • 2
    $\begingroup$ ...unless there is some additional information (such as complete separable metric) so that closed sets may be approximated from inside by compact sets. $\endgroup$
    – Gerald Edgar
    Commented Apr 21, 2013 at 13:30

0

Reset to default

You must log in to answer this question.