No it wasn't.
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Most, if not all, of it is, yes.
I love Lucy was the first show to be taped in front of a live audienceI Love Lucy was the first show sitcom to be taped filmed in front of a live audience.I Love Lucy was on film, therefore it was filmed. Tape was primitive in the 1950s and generally not used if it even existed at the time of I Love Lucy at all.
Yes they actually sometimes talk directly to the audience.
The Cosby Show - Or was that "Sit BooBoo, sit"? TheWikiAnswerMan: I remember Happy Days that stated (at the start of the show) "Filmed before a live studio audience". I think other 70's shows stated that as well. Good Times, maybe? And it was Family Ties that ended the show with "Sit, UBU, sit.".
Filmed live but then edited for TV