I'm getting the out-of-storage space error for Gmail:
Since I'm obviously doing it wrong, what's the correct way to delete all e-mails within a label without creating a filter or deleting the label itself?
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You'll get a message similar to:
All 100 conversations on this page are selected. Select all 75432 conversations
The latter portion is a clickable link. Click it.
It may take a few minutes to move them all to Trash.
If you get an error, you're probably simply trying to do too many at once for your local browser, network, and/or server to handle. (It shouldn't happen, but apparently it does for you.) Try breaking your search up into smaller, but manageable, chunks. There are several advanced search operators you can use. You might try one of the time-based operators, so you can do something like this:
Search for all the messages with your label that are older than a year:
Then follow the other steps above.