As far as I know it makes no difference unless the place is posted (at least in WV) becasue by getting the postal contract it does not make the grocery store a federal building. The Kroger here in Princeton has a 'Post Office' and it is not posted and I have seen a 1 or 2 people carrying in there. (They were 'concealed' carrying, gun in back pocket, I could see the grip but it was technically concealed) and there was no problems, a deputy asked one of them for a concealed permit which he produced and let the man go on his way.
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keep in mind that i am by no means a law expert, i actually know very little about the way the legal system works, just sharing an experience