Real Line - As A Measure Space

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:

    “I have thought a sufficient measure of civilization is the influence of good women.”
    —Ralph Waldo Emerson (1803–1882)

    “The merit of those who fill a space in the world’s history, who are borne forward, as it were, by the weight of thousands whom they lead, shed a perfume less sweet than do the sacrifices of private virtue.”
    —Ralph Waldo Emerson (1803–1882)