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)
“Play is a major avenue for learning to manage anxiety. It gives the child a safe space where she can experiment at will, suspending the rules and constraints of physical and social reality. In play, the child becomes master rather than subject.... Play allows the child to transcend passivity and to become the active doer of what happens around her.”
—Alicia F. Lieberman (20th century)