"Notable" and "noted" are used chiefly of persons or things that are remarkable or distinguished for favorable reasons. Examples: 1) The notable remark will be remembered for a long time. 2) The noted author spoke at a local club.
"Notorious" is now almost always used to mean of ill repute. In other words, if someone is known for doing something bad, he or she is "notorious." Example: The notorious outlaw was hunted by the law.
"Notoriety," likewise, means unfavorable publicity or distinction. Example: She did not want any more notoriety.
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