Is it appropriate to include declined post doc offers on your CV? I have recently got several postdoc offers and two of those were really nice. I have accepted one of them and I am thinking whether I can make some use of the second one that I have turned down.

I traveled quite a long distance to give a job talk, that was pretty successful, and a famous professor in my field made me an offer. Maybe the fact that this famous professor was ready to hire me would make my CV look better (I plan to apply for permanent positions in Academia in Europe/America(s) in future).

So, the question is: would it be helpful and generally acceptable to add to my CV words like "job offer from "Professor_Name" lab, refused in favor of anther offer"? Or it would look like an act of excessive inappropriate boasting?

In general my CV is quite OK even without that so these words would not make a crucial difference anyway, but still.

UPD. My field is applied mathematics/computational neuroscience.
I've seen a few cases of people in my field (linguistics) turning down competitive funding offers and listing them in CVs with "(declined)". Some of these happen to be tied to postdoctoral positions, especially ones offered by governments and/or prestigious granting agencies.

And depending on field/location, it might be possible to list job talks as 'invited talks' for particular departments.

Beyond that, I think referring to job offers you have refused is inappropriate and likely to look only like showing off.