Is it fine to send a message to the author of a paper if I don't understand something and want to clarify it? I'm a Physics Ph.D. student and I have been studying one paper and had some doubt in one point. More specifically the author defines a concept in a way which is a little bit different from other texts I've read before and I'm failing to understand why it is the same thing. I believe I would benefit from understanding this correctly. 

More specifically to the situation, the paper has been posted on arXiv and is really some lecture notes which were latter transformed into a book. The author also says to email any questions or corrections to his email in the first page.


Considering this situation (that it is really some lecture notes later transformed into a book and that the author says to email any questions to his email) is it considered ok to ask it?
More generally, if it is really some paper published in some journal, and if there is nothing written saying that "any questions should be sent to that email", is it still ok to ask of the author in case of any doubts?
My main issue is that I fear if the author might consider my doubt something "too basic". Is that really a problem?
By all means ask. A person who goes through the trouble of writing up lecture notes, is almost certainly a person who would be happy to answer.

As someone who receives a lot of questions from PhD students myself, here are a couple of pointers for how to phrase your question. This could be obvious to you, but I know for sure that it is not obvious for everybody.


If you have a local supervisor, it makes sense to ask them first - maybe it is a trivial question.
Read the paper first, and use the notation from that paper when you can. 
Cut to the chase as quickly as possible. Don't explain their paper back to them in the mail, they know what they wrote.