Title: A Proof of the Herschel-Maxwell Theorem Using the Strong Law of Large Numbers,
Abstract: In this article, we use the strong law of large numbers to give a proof of
the Herschel-Maxwell theorem, which characterizes the normal distribution as
the distribution of the components of a spherically symmetric random vector,
provided they are independent. We present shorter proofs under additional
moment assumptions, and include a remark, which leads to another strikingly
short proof of Maxwell's characterization using the central limit theorem.