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Her voice choking with emotion during an on-court interview, Peng said she had pondered giving up professional tennis in the past, but “my coach, my parents — they always tell me to try to keep going and never ever, give up.”

Peng’s next opponent will be No. 10 Caroline Wozniacki or No. 13 Sara Errani, who met Tuesday night.

In the afternoon, with the temperature topping 90 degrees (32 Celsius) and the humidity at about 50 percent, Monfils and Dimitrov appeared sluggish at times.

“Where should I begin?” said Dimitrov, a Wimbledon semifinalist in July. “Just a bad match for me.”

A key moment came in the second-set tiebreaker, when Dimitrov went ahead 6-4. On the first set point, Dimitrov nearly lost his balance as he shanked a forehand off Monfils’ mediocre drop shot.

“One of the worst drop shots I ever hit,” Monfils said, grinning, “and he hit a frame.”

On the second, a 13-stroke exchange, Dimitrov dropped a backhand into the net.

That was part of four-point run for Monfils thanks to miscues by his opponent. While Monfils essentially kept the ball in play, taking some pace off and pushing shots over the net, Dimitrov sailed forehands long to end the set.

“He defended when he had to,” Dimitrov said. “But if you think about it, I did a lot of unforced errors.”

What mattered in the end, of course, was who won, something that has not always seemed to matter to Monfils.

“For me, tennis is a sport, you know,” he said. “It’s not a job, you know. It’s a sport.”