Google provided "Take out" give you to download all your data from google account. This will show to backup google mail to your local location.

Step-by-step
  1. Login to your google account
  2. Go to you account on the top right of page
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  3. Click "My Account"
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  4. Click "Personal info and privacy"
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  5. Looking for topic Control you content and click "Create Archive"
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  6. Or enter link address TakeOut
  7. Select data to included to backup(This will select only mail)
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  8. Click next to next page
  9. This page will give you to customize download format
    File type: zip, tgz, tbz
    Delivery Method: Send download link via email(Download to local space), Add to drive(Depend on your quota space)
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  10. Select .zip file type and send download link via email (Download to local computer)
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  11. Google will preparing archive your mail data. Mail archive may take a long time (hours or possibly days) to create. (Depend on number of your emails)
  12. When it prompt to download it will show download button.
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  13. Click "Download"
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  14. After finish will get file .zip, Double click to open you will see file .mbox inside.
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  15. All mail data already on your local in .mbox file type.