If there are records showing for the number of records successfully processed but a quantity of zero is showing in the Export outputs section, this issue is most likely caused from a Membership renewal email and export definition being used instead of a Direct marketing email.  Recreate the email in Marketing and Communications as a Direct marketing email, add it to a Package, and use this Package in the Event invitations.  Delete the most recent History from the Event invitation process, run the process again, and you should be able to successfully send the emails.