Is it "allowed" to write that someone is dead (in fiction) when he/she is not, but the MC believes it so?

I've always struggled with this. In first person it's simple; if the MC thinks that someone is dead, it can just be said, "Such and such is dead," because it's the MC talking. But in third person, the narrator knows everything. I can't write "Such and such is believed to be dead" because that implies that he/she is really alive and the reader isn't supposed to know. To get by, I've been playing with euphemisms, but that doesn't work great. I'm trying to think of books when someone was found not to be dead, but all I can come up are first person examples.