The active plasma lens represents a compact and affordable tool with radially symmetric focusing and field gradients up to several kT/m. In order to be used as a focusing device, its effects on the particle beam distribution must be well characterized. Here, we present the experimental results obtained by focusing an high-brightness electron beam by means of a 3 cm-long discharge-capillary pre-filled with Hydrogen gas. We achieved minimum spot sizes of 24 lm (rms) showing that, during plasma lensing, the beam emittance increases due to nonlinearities in the focusing field. The results have been cross-checked with numerical simulations, showing an excellent agreement