The hypothesis is that, for 
is a measure space, 
for each 
, as 
. The hypothesis may be weakened to almost
everywhere convergence.
Pointwise Convergence
See also
Almost Everywhere ConvergenceExplore with Wolfram|Alpha
References
Browder, A. Mathematical Analysis: An Introduction. New York: Springer-Verlag, 1996.Referenced on Wolfram|Alpha
Pointwise ConvergenceCite this as:
Weisstein, Eric W. "Pointwise Convergence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PointwiseConvergence.html