There's a stronger version of that theorem due to Lyapunov. It is stronger because it concerns vectors of measures, and not only a single measure. It states that given a non-atomic vector measure (a collection of $n$ measures $\mu_1,\ldots, \mu_n$ where each measure is non-atomic) always has an image which is convex (in $\mathbb{R}^n$).

Unfortunately, I could never find a translation of his paper, so I can only link the [version in russian][1]. The main statements can be found in French at the end of the paper. There's also a [paper of Halmos][2] that proves the result.

I think the result for vector measures is much harder to prove, but if what you want is a reference so you don't have to prove the result yourself, it serves the purpose.


  [1]: http://www.mathnet.ru/links/e8bebeff1522d3398898112145091ef2/im3907.pdf
  [2]: http://www.ams.org/journals/bull/1948-54-04/S0002-9904-1948-09020-6/S0002-9904-1948-09020-6.pdf