Lebesgue integral over a subset of the measure space
Let be a measure space and .
Let be a measurable function and
. Then is defined as .
By the properties of the Lebesgue integral of nonnegative measurable functions (property 3), we have that .
Let be a measurable function such that not both of and are infinite. (Note that and are defined in the entry Lebesgue integral.) Then is defined as .
|Title||Lebesgue integral over a subset of the measure space|
|Date of creation||2013-03-22 16:13:54|
|Last modified on||2013-03-22 16:13:54|
|Last modified by||Wkbj79 (1863)|