You may think one can distinguish two quite different problems here.
1. How do we think of these sets of perceptions as belonging to an enduring object.
and
2. How do we think of these sets of perceptions as belonging to something which exists objectively?
You might like to consult Jonathan Bennett (Locke, Berkeley Hume, 1971, Oxford) for help in understanding how Hume is to be understood as making this distinction and then addressing the two problems.
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