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:
“Trying to love your children equally is a losing battle. Your children’s scorecards will never match your own. No matter how meticulously you measure and mete out your love and attention, and material gifts, it will never feel truly equal to your children. . . . Your children will need different things at different times, and true equality won’t really serve their different needs very well, anyway.”
—Marianne E. Neifert (20th century)
“Here in the U.S., culture is not that delicious panacea which we Europeans consume in a sacramental mental space and which has its own special columns in the newspapers—and in people’s minds. Culture is space, speed, cinema, technology. This culture is authentic, if anything can be said to be authentic.”
—Jean Baudrillard (b. 1929)