L² space

An L² space is a collection of functions where the total of their squared values (integrated over a domain) is finite. Think of it as functions that, when you square their output and sum these squares across the entire domain, result in a manageable, finite number. This concept is crucial in areas like quantum mechanics and signal processing because it helps analyze functions that are "square-integrable," ensuring their overall energy or magnitude remains finite. Essentially, L² space provides a structured framework to work with functions that are well-behaved in terms of their size and energy.