Pushforward measure

A size is a term from the mathematical branch of measure theory and is used to transfer the measurement in a measure space to another space. Here, using a measurable function assigned to the quantities in values ​​. The so defined to measure the size.

An important role is played by the size especially in the definition of the probability distribution of a random variable.

Definition

Be a measure space and a - measurable function in a measurement space. Then

A measure on the size of. Here, the archetype described by.

Example of use

For a measurable function (the extended real numbers ) represented by the following transformation theorem holds for measurable quantities:

If at least one of the above two integrals is defined.

Swell

• Measure theory