Inner regular measure: Difference between revisions

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This property is sometimes referred to in words as "approximation from within by compact sets."
 
Some authors<ref name="AGS">{{cite book | author=Ambrosio, L., Gigli, N. & Savaré, G. | title=Gradient Flows in Metric Spaces and in the Space of Probability Measures | publisher=ETH Zürich, Birkhäuser Verlag | ___location=Basel | year=2005 | id=ISBN 3-100717643-24242428-7 }}</ref> use the term '''tight''' as a [[synonym]] for inner regular. This use of the term is closely related to [[Tightness of measures|tightness of a family of measures]], since a measure ''&mu;'' is inner regular [[if and only if]], for all ''&epsilon;'' &gt; 0, there is some [[compact space|compact subset]] ''K'' of ''X'' such that
 
:<math>\mu \left( X \setminus K \right) < \varepsilon.</math>