Lebesgue Measure - Definition

Definition

Given a subset, the Lebesgue outer measure is defined as


.


The Lebesgue measure of E is given by its Lebesgue outer measure if, for every ,

.

Read more about this topic:  Lebesgue Measure

Famous quotes containing the word definition:

    One definition of man is “an intelligence served by organs.”
    Ralph Waldo Emerson (1803–1882)

    It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.
    François, Duc De La Rochefoucauld (1613–1680)

    Was man made stupid to see his own stupidity?
    Is God by definition indifferent, beyond us all?
    Is the eternal truth man’s fighting soul
    Wherein the Beast ravens in its own avidity?
    Richard Eberhart (b. 1904)