Lebesgue Spaces

Lebesgue spaces, often denoted as \(L^p\) spaces, are mathematical frameworks used to analyze functions based on how their values behave over a domain. They measure the size or "magnitude" of functions using integrals, specifically focusing on the p-th power of the absolute value of the functions. For example, in \(L^2\), functions have finite energy, meaning the integral of their square is finite. These spaces help mathematicians understand and compare functions, especially in contexts like signal processing or probability, by providing a rigorous way to quantify their "length" or "size" in a generalized sense.