2007-02-13 01:54:56 · 2 answers · asked by malay_jam07 1 in Science & Mathematics ➔ Mathematics
That's Lebesgue measure. The answer to this question depends a bit on context. The Lebesgue measure on the line is simply a generalization of the concept of length. It is also possible to talk about Lebesgue measure on the plane or in higher dimensions. In those cases, you get generalizations of area or volume.
Lebesgue measure is used to construct the Lebesgue integral, which is a generalization of the Riemann integral that is taught in calculus classes. The Lebesgue integral has much nicer behavior under limits than the Riemann does.
2007-02-13 03:02:47 · answer #1 · answered by mathematician 7 · 2⤊ 0⤋
The extension of concepts like length and area to things less obvious than lines and polygons. Read about it here:
http://mathworld.wolfram.com/LebesgueMeasure.html
2007-02-13 02:00:00 · answer #2 · answered by Anonymous · 0⤊ 1⤋