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:
“From whatever you wish to know and measure you must take your leave, at least for a time. Only when you have left the town can you see how high its towers rise above the houses.”
—Friedrich Nietzsche (1844–1900)
“Let the space under the first storey be dark, let the water
lap the stone posts, and vivid green slime glimmer
upon them; let a boat be kept there.”
—Denise Levertov (b. 1923)