As anticipated, mayoral candidate Bill Thompson easily won the Democratic city primary yesterday, taking 70 percent of the vote. His closest rival, Tony Avella, took a mere 23 percent. Thompson will go on to challenge Mayor Bloomberg, who is running as an independent and also on the Republican party line, in the general election. Meanwhile, Cyrus Vance, the Robert Morgenthau–appointed candidate for district attorney, won that race with 44 percent of the vote. His chief rival, Leslie Crocker Snyder, who previously ran against Morgenthau, garnered 30 percent. In the race for comptroller, the results were too close to call. Candidates David Yassky and John Liu (who, we couldn’t help but notice, continued to run campaign ads that claimed he worked in a sweatshop as a child long after it was reported they were untrue) will have a runoff on September 29. Liu had 38 percent of the vote to Yassky’s 30, which didn’t break the 40 percent needed for a win. And in the race for public advocate, there will also be a runoff between Bill de Blasio and Mark Green, who formerly held the position for seven years.