As A Measure Space
The real line carries a canonical measure, namely the Lebesgue measure. This measure can be defined as the completion of a Borel measure defined on R, where the measure of any interval is the length of the interval.
Lebesgue measure on the real line is one of the simplest examples of a Haar measure on a locally compact group.
Read more about this topic: Real Line
Famous quotes containing the words measure and/or space:
“Speech is the twin of my vision, it is unequal to measure itself,
It provokes me forever, it says sarcastically,
Walt you contain enough, why don’t you let it out then?”
—Walt Whitman (1819–1892)
“This moment exhibits infinite space, but there is a space also wherein all moments are infinitely exhibited, and the everlasting duration of infinite space is another region and room of joys.”
—Thomas Traherne (1636–1674)