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I try to understand a SPV implementation.
I read the wiki pages on Protocol Specification and Thin Client Security as well as the white-paper's chapter 8 .
What I don't understand:
Assume user A has Bitcoin address X.
User A can do getheaders and load all block headers and then have all block hashes and timestamps.
So: how does a SPV client then find possible transactions to the user's Bitcoin address X without loading all blocks (and all transactions)?

1But how does Multibit (a SPV thin-client) check for incomming payments so fast? – Jonas Schnelli – 2013-05-20T06:48:31.383
@Jonas, Multibit uses bloom filters, that why it can check for incomming payments that fast. – rdymac – 2013-05-20T20:53:47.460
2I downvoted. Verifying transaction is exactly the thing SPV does not do: it only verifies the block chain, not the transactions in it. – Pieter Wuille – 2013-06-19T09:36:02.127
SPV clients can calculate balances and can list transactions to certain addresses by requesting filtered blocks. SPV clients also verify transaction validity by verifying the signatures; what SPV does not verify is inclusion of outputs in the utxo, so double spending is possible. – dionyziz – 2016-01-25T00:02:33.470
@dionyziz SPV clients cannot verify signatures, as they don't have the UTXO entries to know what to verify against. – Pieter Wuille – 2016-09-05T17:17:31.367
@Pieter Thanks for clarifying, you are correct. – dionyziz – 2016-09-06T00:11:59.277