Measurable Function

In the measure space

, consider

are real numbers.
If

is the sum of a finite number of sets, then

is denominated simple function.
If

is a real number and

, then

is denominated measurable function.

Properties
Let

be a real number. We have

Complex function
If

is a complex function defined in

and both its real and imaginary parts are measurable, then

is a measurable function.

[0]Top