A generalization of the Lebesgue integral. A measurable function 
is called 
-integrable over the closed interval ![[a,b]](https://mathworld.wolfram.com/images/equations/A-Integrable/Inline3.svg)
if
 | (1) |
where 
is the Lebesgue measure, and
![I=lim_(n->infty)int_a^b[f(x)]_ndx](https://mathworld.wolfram.com/images/equations/A-Integrable/NumberedEquation2.svg) | (2) |
exists, where
![[f(x)]_n={f(x) if |f(x)|<=n; 0 if |f(x)|>n.](https://mathworld.wolfram.com/images/equations/A-Integrable/NumberedEquation3.svg) | (3) |
A-Integrable
Explore with Wolfram|Alpha
References
Titchmarsh, E. C. "On Conjugate Functions." Proc. London Math. Soc. 29, 49-80, 1928.Referenced on Wolfram|Alpha
A-IntegrableCite this as:
Weisstein, Eric W. "A-Integrable." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/A-Integrable.html