An integrable function is one whose integral exists as a finite value in the sense under consideration.
For the Lebesgue integral (Hunter 2011, pp. 42 and 50), a measurable function 
or 
is integrable with respect to a positive
measure 
iff
 |
Integrable
See also
Differentiable, Integrable Differential Ideal, Integral, Integration, Lebesgue Integral, Locally Integrable, Square IntegrableExplore with Wolfram|Alpha
References
Hunter, J. K. Measure Theory. Lecture notes, pp. 42 and 50-51, 2011. https://www.math.ucdavis.edu/~hunter/measure_theory/measure_notes.pdf.Referenced on Wolfram|Alpha
IntegrableCite this as:
Weisstein, Eric W. "Integrable." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Integrable.html