L²空間, or L² space, is a mathematical concept used in functional analysis and is part of the broader field of Hilbert spaces. It consists of all square-integrable functions, meaning that the integral of the square of the function's absolute value is finite. This space is essential for various applications in quantum mechanics and signal processing. In L² space, functions can be treated as vectors, allowing for the use of geometric concepts like distance and angle. The inner product in L² space is defined as the integral of the product of two functions, which helps in determining orthogonality and convergence of functions, making it a powerful tool in mathematics and engineering.