L² spaces, also known as "square-integrable" spaces, are a type of function space in mathematics. They consist of all functions for which the integral of the square of the absolute value is finite. This means that if you take a function f, the integral of |f(x)|² over its domain must be a finite number. L² spaces are crucial in various fields, including quantum mechanics and signal processing, as they provide a framework for analyzing functions and signals. In L² spaces, functions can be treated as vectors, allowing the use of geometric concepts like distance and angle. The inner product in L² spaces is defined as the integral of the product of two functions, which helps in determining orthogonality and projection. This structure makes L² spaces a fundamental part of functional analysis and Hilbert spaces, enabling the study of convergence and continuity in a rigorous way.