Assertion: measure | /r/HasProperty | inner regular
Facets:
Source sentences:
text: This measure is inner regular and locally finite, but is not outer regular as any open set containing the y-axis has measure infinity.
text: A measure is called inner regular if every measurable set is inner regular.
text: A measure is called outer regular if every measurable set is outer regular.
text: The measure m is called a Radon measure if it is inner regular, outer regular and locally finite.
text: Measures that are neither inner nor outer regular [ edit ]
text: The measure that assigns measure 1 to Borel sets containing an unbounded closed subset of the countable ordinals and assigns 0 to other Borel sets is a Borel probability measure that is neither inner regular nor outer regular.
text: The measure m is called a Radon measure if it is inner regular, outer regular and locally finite.
text: This measure is inner regular and locally finite, but is not outer regular as any open set containing the y-axis has measure infinity.
text: Some authors use a different definition: a measure is called inner regular if every open measurable set is inner regular.
text: The measure m is called inner regular or tight if, for any open set U, m(U) is the supremum of m(K) over all compact subsets K of U.
text: A measure is called regular if it is outer regular and inner regular.