  The nearby ultra-luminous infrared galaxy (ULIRG) Arp 220 is an excellent
laboratory for studies of extreme astrophysical environments. For 20 years,
Very Long Baseline Interferometry (VLBI) has been used to monitor a population
of compact sources thought to be supernovae (SNe), supernova remnants (SNRs)
and possibly active galactic nuclei (AGNs). Using new and archival VLBI data
spanning 20 years, we obtain 23 high-resolution radio images of Arp 220 at
wavelengths from 18 cm to 2 cm. From model-fitting to the images we obtain
estimates of flux densities and sizes of all detected sources. We detect radio
continuum emission from 97 compact sources and present flux densities and sizes
for all analysed observation epochs. We find evidence for a LD-relation within
Arp 220, with larger sources being less luminous. We find a compact source LF
$n(L)\propto L^\beta$ with $\beta=-2.19\pm0.15$, similar to SNRs in normal
galaxies. Based on simulations we argue that there are many relatively large
and weak sources below our detection threshold. The observations can be
explained by a mixed population of SNe and SNRs, where the former expand in a
dense circumstellar medium (CSM) and the latter interact with the surrounding
interstellar medium (ISM). Nine sources are likely luminous, type IIn SNe. This
number of luminous SNe correspond to few percent of the total number of SNe in
Arp 220 which is consistent with a total SN-rate of 4 yr$^{-1}$ as inferred
from the total radio emission given a normal stellar initial mass function
(IMF). Based on the fitted luminosity function, we argue that emission from all
compact sources, also below our detection threshold, make up at most 20\% of
the total radio emission at GHz frequencies.
