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==Definition==
Let <math>(X, \mathcal{T})</math> be a [[topological space]]; let <math>(X, \mathcal{A}, \mu)</math> also be a [[measure space]] such that the [[sigma algebra]] <math>\mathcal{A}</math> contains all open sets <math>U \in \mathcal{T}</math>. Then the '''support''' of the measure <math>\mu</math> is defined to be the set of all points <math>x \in X</math> for which every [[Open_set|open]] [[Neighbourhood_(mathematics)|neighbourhood]] of <math>x</math> has [[positive]] measure:
:<math>\mathrm{supp} (\mu) := \{ x \in X | \forall x \in N_{x} \in \mathcal{T}, \mu (N_{x}) > 0 \}.</math>
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