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Screenshot from textbook

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?

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I believe the second parts should read $$ L(\hat{\theta}) = \max_{\theta} L(\theta) $$ and $$ l(\hat{\theta}) = \max_{\theta} l(\theta) $$

As written, it doesn't make sense.

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