I am interested in finding the extreme points of the following set of distributions 
\begin{align}
\mathcal{P}= \left\{F: \int_{\mathbb{R}} |x|^k dF(x)=c \right\}
\end{align}
where $k,c>0$. 

I know that [this paper][1] by Winkler is a standard reference on this question. 

I was trying to extract the answer from this paper and got that the set of extreme points is given by 
\begin{align}
\mathop{\rm ex}(\mathcal{P}) = \left\{F \in \mathcal{P} : F= (1-t) \delta_{x_1}+t \delta_{x_2}, t\in[0,1], x_1,x_2 \in \mathbb{R} \right\}.
\end{align}

However, not sure if this is correct since in [this question][2], for a very similar set, it was pointed out that it must be combination of three mass points instead of two.  


  [1]: https://www.jstor.org/stable/pdf/3689944.pdf?refreqid=excelsior%3A6c1f2a909f95192f8b30edf1e31ad3de
  [2]: https://mathoverflow.net/questions/85527/extreme-points-of-a-set-of-probability-measures