If 
is the Borel
sigma-algebra on some topological space,
then a measure 
is said to be a Borel measure (or Borel probability
measure). For a Borel measure, all continuous functions are measurable.
Borel Measure
See also
Regular Borel MeasureExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Borel Measure." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BorelMeasure.html