So if have a bitcoin core wallet app,does it mean i own the address/es shown on the app?

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Yep, you got it! If an address shows up in your Bitcoin Core wallet, that means it's yours. Your wallet app holds the private keys for those addresses, which is like having the keys to a safe.

Just remember: whoever has the private keys owns the coins at those addresses. Keep 'em secure and backup your wallet to protect your Bitcoin stash!

So even the balances are mine?