Under 'general remarks' on maximum likelihood estimators. I don't understand the right hand side of ii. (it is also repeated in iii. this time as the log-likelihood function). That the MLE is theta hat equals arg-theta-max makes sense but why does the likelihood function of theta hat also equal arg-theta-max? Doesn't this imply that theta-hat equals its own likelihood function? This doesn't make sense to me. Should it?