  We discuss a general definition of likelihood function in terms of
Radon-Nikod\'{y}m derivatives. The definition is validated by the Likelihood
Principle once we establish a result regarding the proportionality of
likelihood functions under different dominating measures. This general
framework is particularly useful when there exists no or more than one obvious
choice for a dominating measure as in some infinite-dimensional models. We
discuss the importance of considering continuous versions of densities and how
these are related to the Likelihood Principle and the basic concept of
likelihood. We also discuss the use of the predictive measure as a dominating
measure in the Bayesian approach. Finally, some examples illustrate the general
definition of likelihood function and the importance of choosing particular
dominating measures in some cases.
