Support (measure theory)

In mathematics, the support (sometimes topological support or spectrum) of a measure ${\displaystyle \mu }$ on a measurable topological space ${\displaystyle (X,\operatorname {Borel} (X))}$ is a precise notion of where in the space ${\displaystyle X}$ the measure "lives". It is defined to be the largest (closed) subset of ${\displaystyle X}$ for which every open neighbourhood of every point of the set has positive measure.