I study the subject of fair division (cake-cutting), and many papers contain a reference to a theorem by Lyapunov, which states that the range of any real-valued, non-atomic vector measure is compact and convex.

Can you recommend an online resource that can help me understand this theorem in an intuitive fashion, without having to read an entire book or take an entire course?

Note: I am not looking to become an expert in this field; I just want to get some intuition about this theorem, so that I can understand the papers that rely on it.