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)
“At first thy little being came:
If nothing once, you nothing lose,
For when you die you are the same;
The space between, is but an hour,
The frail duration of a flower.”
—Philip Freneau (1752–1832)