| Résume | Quantitative Measured Subgroups have been introduced by Tessera, Le Maître, Delabie and Koivisto as a quantitative asymmetric analogue of Measure Equivalence for discrete groups. In this talk, I will introduce the same notion for locally compact compactly generated unimodular groups, proving the monotonicity of the isoperimetric profile in the locally compact case as well as the existence of a quantitative measured subgroup coupling from a regular embedding between locally compact groups (this is a measured analogue of coarse embedding between groups). As a consequence of this, I will finish by proving the monotonicity of the isoperimetric profile for regular embeddings between locally compact compactly generated unimodular groups. |
