L^p spaces

L^p spaces are mathematical collections of functions where the "size" or "magnitude" of each function is measured using a specific way called the p-norm. For a function, this involves raising its values to the power of p, integrating over its domain, and then taking the p-th root. These spaces allow mathematicians to analyze functions based on how their values are distributed, with different values of p emphasizing different aspects—like peak values or overall behavior. L^p spaces are fundamental in fields like engineering, physics, and mathematics, providing a structured way to study functions with various integrability and smoothness properties.