Lebesgue Spaces are mathematical structures that generalize the concept of measuring size or volume in a way that accommodates more complex sets than traditional methods. They are defined using a measure, specifically the Lebesgue Measure, which allows for the integration of functions over these sets. These spaces are denoted as L^p spaces, where "p" is a positive real number. Functions in L^p spaces are those whose p-th power is integrable, meaning their total size can be calculated. This framework is essential in various fields, including functional analysis and probability theory.