Lebesgue Measure

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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: