<P> In mathematics and in particular measure theory , a measurable function is a function between two measurable spaces such that the preimage of any measurable set is measurable , analogously to the definition that a function between topological spaces is continuous if the preimage of each open set is open . In real analysis , measurable functions are used in the definition of the Lebesgue integral . In probability theory , a measurable function on a probability space is known as a random variable . </P>
<P> In mathematics and in particular measure theory , a measurable function is a function between two measurable spaces such that the preimage of any measurable set is measurable , analogously to the definition that a function between topological spaces is continuous if the preimage of each open set is open . In real analysis , measurable functions are used in the definition of the Lebesgue integral . In probability theory , a measurable function on a probability space is known as a random variable . </P>
when is a function said to be measurable
when is a function said to be measurable
a function between two measurable spaces such that the preimage of any measurable set is measurable
a function between two measurable spaces such that the preimage of any measurable set is measurable