The Minkowski Inequality is a fundamental result in mathematics, particularly in the field of functional analysis and normed vector spaces. It states that for any two vectors in a normed space, the norm of their sum is less than or equal to the sum of their norms. This can be expressed mathematically as: ||x + y|| \leq ||x|| + ||y|| , where x and y are vectors and ||\cdot|| denotes the norm. This inequality is essential for proving various properties of L^p spaces, which are important in areas such as probability theory and statistics. The Minkowski Inequality helps establish the concept of distance in these spaces, allowing for a better understanding of convergence and continuity in mathematical analysis.