Strong and Weak Convergence

Strong and weak convergence are concepts in mathematics that describe how a sequence of functions or numbers approach a limit. Strong convergence means each element in the sequence gets very close to the limit itself, in a direct, measurable way. Weak convergence means the sequence approaches the limit in a less direct sense, often only when tested against specific functions or criteria. In simpler terms, strong convergence is like getting close to a point with each step, while weak convergence is more about the overall trend or behavior, even if individual steps aren’t as close.