Definition:Mean Value over Measure

Definition

Let $\struct {X, \Sigma, \mu}$ be a measure space.

Let $f$ be a $\mu$-integrable function on a domain $D$.

The mean value of $f$ on $D$ is defined as:

$\ds \frac 1 {\map \mu D} \int_D \map f \rd \mu$

Also see

• Definition:Mean Value of Function

• Results about mean value over measure can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): mean value (of a function)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): mean value (of a function)