Only 98,600 people wrote messages on Twitter about the two-hour season premiere of “Grey’s Anatomy” last month. That’s a tiny fraction of the 9.3 million who, according to Nielsen, watched the show that night. But the posts, 225,000 of them in total, were seen by millions of Twitter users, some of whom might have fired up their digital video recorders or laptops to watch the episode later. Nielsen is now measuring what it calls the “unique audience” for Twitter posts about television, providing a more complete view of the phenomenon known as social TV. On Monday the company is introducing Nielsen Twitter TV Ratings, a product announced last year that professes to measure all the activity and reach of Twitter conversation about shows, even if it has yet to be embraced by television executives and gain a broad client base. “We feel this is going to be a credibility-building moment for the industry,” said Andrew Somosi, the chief executive of SocialGuide.