Biases on initial mass function determinations. II. Real multiple   systems and chance superpositions
  When calculating IMFs for young clusters, one has to take into account that (a) most massive stars are born in multiple systems (b) most IMFs are derived from data that cannot resolve such systems, and (c) multiple chance superpositions between members are expected to happen if the cluster is too distant. In this article I use numerical experiments to model the consequences of those phenomena on the observed color-magnitude diagrams and the IMFs derived from them. Real multiple systems affect the observed or apparent massive-star MF slope little but can create a significant population of apparently ultramassive stars. Chance superpositions produce only small biases when the number of superimposed stars is low but, once a certain number threshold is reached, they can affect both the observed slope and the apparent stellar upper mass limit. I apply those experiments to two well known massive young clusters in the Local Group, NGC 3603 and R136. In both cases I show that the observed population of stars with masses above 120 solar masses can be explained by the effects of unresolved objects, mostly real multiple systems for NGC 3603 and a combination of real and chance-alignment multiple systems for R136. Therefore, the case for the reality of a stellar upper mass limit at solar or near-solar metallicities is strengthened, with a possible value even lower than 150 solar masses. An IMF slope somewhat flatter than Salpeter or Kroupa with gamma between -1.6 and -2.0 is derived for the central region of NGC 3603, with a significant contribution to the uncertainty arising from the imprecise knowledge of the distance to the cluster. The IMF at the very center of R136 cannot be measured with the currently available data but the situation could change with new HST observations. (abridged) 
J. Ma\'iz Apell\'aniz