Lebesgue Space

Definition


Lebesgue space {% L^2[0,1] %} is the set of Lebesgue Measurable complex valued functions on the closed interval {% [0,1] %}. Functions that are equal almost everywhere are identified as a single element of the space.

Theorems


  • {% C[0,1] %} (continuous functions on {% [0,1] %}) is dense in {% L^2[0,1] %}