measurable function
A "measurable function" is crucial in measure theory, allowing the integration and analysis of functions within mathematics.
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Definition
C1Measure Theory
(technical, academic)A function between two measurable spaces where the preimage of any measurable set in the target space is measurable in the source space.
Example
- In probability theory, random variables are modeled as measurable functions.
C1Real Analysis
(technical, academic)A function from a measurable set to the real numbers, ensuring the preimage of every Borel set is measurable.
Example
- The function f(x) = x^2 is measurable when considered on the set of real numbers.
Similar
Terms that have similar or relatively close meanings to "measurable function":