According to google one of the meanings of the word epitome is:a summary of a written work; an abstract. So can I use this word to say "This theorem is the epitome of this lecture". Is this usage correct?
"Epitome" is used in the post in such a way, that it fails to convey the intended meaning.
EPITOME means summary, synopsis or 'sum and substance' and we are habituated to use "epitomise" in the same way as we use 'summarise'.
It seems the entire lecture is elucidating a theorem. "--" text should be given a rendering the other way round so that it can bring out the actual meaning of epitome.
I think I found similar usage from usage of the word epitome
But "an epitome" would mean "an abstract."
An epitome of what has been written on this subject will be found in chapter 3.
"Epitome" is more than a summary, a synopsis or an abstract: it's an abbreviated version of a written work.
Reader's Digest publishes every month epitomes of articles appearing in a wide variety of journals or books.
Saying "this theorem is the epitome of this lecture" is then unappopriate: the theorem may be the core of the document, but it is not a reduced/shortened version of the text.