On a measure space X, the set of square integrable L^2-functions is an L^2-space. Taken together with the L^2-inner product with respect to a measure μ, 〈f, g〉 = integral_X f g d μ the L^2-space forms a Hilbert space.

completion | Hilbert space | L^2-function | L^2-inner product | L^2-norm | Lebesgue integral | Lebesgue measure | L^p-space | measure | measure space | Riesz-Fischer theorem | Schwarz's inequality