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What is the dual of the space of all vector valued Borel measures?

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  • $\begingroup$ What kind of underlying topological space should the borel measures have? A polish space? A locally compact space? Something else? $\endgroup$
    – Johannes Hahn
    Commented Oct 23, 2013 at 17:26
  • $\begingroup$ See math.stackexchange.com/q/74875/442 for signed measures. What do you mean with both "vector valued" and "signed" at the same time? $\endgroup$
    – Gerald Edgar
    Commented Oct 23, 2013 at 17:37
  • $\begingroup$ Assume that the space is equipped with the total variation norm. $\endgroup$
    – Weymon He
    Commented Oct 23, 2013 at 17:43
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    $\begingroup$ So presumably the values are in some normed space? $\endgroup$
    – Gerald Edgar
    Commented Oct 23, 2013 at 18:32
  • $\begingroup$ @WeymonHe: You misunderstood. Your measures are maps $\mathfrak{B}(X)\to V$ for some topological space X and some vector space V. My question concerns X. Do want to impose any restrictions on X like being a polish space etc.? $\endgroup$
    – Johannes Hahn
    Commented Oct 23, 2013 at 18:33

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