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What does it mean to be in public domain

That question is answered by the first sentence on the page that this thread is discussing:

> At the start of each year, on January 1st, a new crop of works enter the public domain and become free to enjoy, share, and reuse for any purpose.

that the Hitler estate can't sue you for copyright infringement if you publish it yourself and distribute copies.

Interesting that he still has an estate. And thanks for explaining what it means

In practice, there was not a Hitler estate - the government of Bavaria (a state in Germany) took ownership of the copyright.

...did they exercise it?

Rather the opposite, they disallowed anyone from printing copies

Estate is a common law concept. There’s no direct equivalent in German law.