A Borel measure on a topological space 
is a measure
defined on its Borel sigma-algebra 
, with values in ![[0,infty]](/images/equations/BorelMeasure/Inline3.svg)
. It is a Borel probability
measure when its total measure is 1. Every continuous
function between topological spaces is a
measurable function when both spaces are equipped
with their Borel sigma-algebras.
Borel Measure
See also
Borel Sigma-Algebra, Measure, Probability Measure, Regular Borel MeasureExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Borel Measure." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BorelMeasure.html