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Suppose I generate an address offline, using something like bitaddress.org

And then I receive some bitcoins on this address.

How do I know how much balance do I have on this address?

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Whether an address was generated online or offline is irrelevant.

Any transaction that sends bitcoin to the address will be included in a block once it gets mined.

You can check the address balance by searching for that address in a block explorer such as https://blockexplorer.com/

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