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Verify partial message given hash of full message

I need to verify partial downloads (retrieved sequentially), given a (preferably short) hash of the complete download.

Is there a construct that can do that, even a probabilistic one?

EDIT: clarify the bits about 'preferably short'. Hash tree adds space burden to transmit O(2*n) hashes. Hash list is O(n). I'm looking for O(1) space requirement.