pointwise convergence

Pointwise convergence describes a situation where a sequence of functions approaches a specific function at each individual point in its domain. In other words, for every point you choose, the values of the functions in the sequence get closer and closer to the value of a target function at that exact point as the sequence progresses. This means that, although the whole sequence may not uniformly approximate the target function everywhere at once, at every single point, the functions settle closer and closer to it individually.