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Does delivery report mean that the person reads the message on android phone?
No, delivery reports generally just tell you that the message has been delivered and is sitting on their phone. It does not necessarily tell you that they've been read. There isn't a way to tell if its been read as far as I know.
Numerous Messenger apps provide the possibility to see if a person has read your message.
For text messages though, it is not possible to get a read status as it is not part of the SMS protocol.