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*On the null-set lamination space.*

## Résumé

After recalling the notion of measured geodesic lamination on a given closed hyperbolic surface, we will define a new set called the null-set lamination space and following a Ivanov result we shall prove a rigidity result.

I will discuss how this quantity is related to another one:
the exponential rate of growth of the volume of a ball in the Hilbert metric
on the convex body.

This is joint work with Constantin Vernicos.