Lebesgue Measure Article Index for
Lebesgue
Website Links For
Lebesgue
 

Information About

Lebesgue Measure





EXAMPLES

  • If ''A'' is a closed interval ''b'' , then its Lebesgue measure is the length ''b''−''a''. The open interval (''a'', ''b'') has the same measure, since the difference between the two sets has measure zero.

  • If ''A'' is the Cartesian Product of intervals ''b'' and ''d'' , then it is a rectangle and its Lebesgue measure is the area (''b''−''a'')(''d''−''c'').

  • The Cantor Set is an example of an Uncountable Set that has the Lebesgue measure of zero.



PROPERTIES

The Lebesgue measure on R''n'' has the following properties: