This story draft by @keynesian has not been reviewed by an editor, YET.
Authors:
(1) Edward Crane, School of Mathematics, University of Bristol, BS8 1TH, UK;
(2) Stanislav Volkov, Centre for Mathematical Sciences, Lund University, Box 118 SE-22100, Lund, Sweden.
Reduction to the case of uniform geometry
All original points are eventually removed, a. s.
Acknowledgements and References
This paper is available on arxiv under CC 4.0 license.
5 In fact one could obtain F(X) − F({z} ∪ (X \ {xk})) ≥ (1−α)(M+1) M2 F(X), but the simpler lower bound given in (14) will suffice for the applications.