Plain Language Summary How to deal with the fact that resilience cannot be measured at agiven scale, but accross scales? The answer requires to combine two theoretical frameworks: multifractals and the teory of viability. The term resilience has become extremely fashionable and there had been many attempts to provide operational definition and in fact metrics going beyond a set of more or less ad-hoc indicators. The viability theory (Aubin and Saint-Pierre, 2011) have been used to give a rather precise mathematical definition of resilience (Deffuant and Gilbert, 2011). However, it does not grasp the multiscale nature of resilience that is rather fundamental as particularly stressed by Folke et al (2010). In this communication, we first recall a preliminary attempt (Tchiguirinskaia et al., 2014) to define multifractal resilience with the help of the maximal probable singularity. Then we extend this multifractal approach to the capture basin of the viability, therefore the resilient basin. Aubin, J P, A. Bayen, and P Saint-Pierre (2011). Viability Theory. New Directions. Springer, Berlin,. Deffuant, G. and Gilbert, N. (eds) (2011) Viability and Resilience of Complex Systems. Springer Berlin. Folke, C., S R Carpenter, B Walker, M Sheffer, T Chapin, and J Rockstroem (2010). Resilience thinking: integrating re- silience, adaptability and transformability. Ecology and So- ciety, 14(4):20, Tchiguirinskaia,I., D. Schertzer, , A. Giangola-Murzyn and T. C. Hoang (2014). Multiscale resilience metrics to assess flood. Proceedings of ICCSA 2014, Normandie University, Le Havre, France -