Serena Williams, Sloane Stephens win in fourth round of US Open

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Asked if she was considering having another child, Williams said: "I've obviously thought about having more kids and it will happen, God willing, in time".

Williams, whose daughter Olympia turned one on Saturday, is aiming to win a record-equalling 24th Grand Slam title in NY. "She's had a lot of good wins in her career. I was just happy to get through it to be honest".

"That desire has not gone down at all and I don't think it was capable of going up, because if it was at a 10, I felt I was at a 15 or a 20 and I'm still there", said Williams of her will to win. "I think that was a great point".

Serena Williams' U.S. Open win over Kaia Kanepi was tough, probably tougher than expected.

Serena Williams at the US Open on 28 August 2018.

Meanwhile, defending men's champion Rafael Nadal beat Nikoloz Basilashvili Sunday 6-3 6-3 6-7 (6-8) 6-4 and will next face Dominic Thiem in the quarterfinals.

Williams has never dropped a set in four previous meetings with Kanepi, the last of which was at the 2014 U.S. Open, but the Estonian is high on confidence after eliminating top seed Simona Halep in the first round.

The importance of a hard-fought hold for Williams at the start of the third was highlighted by a loud cry from the American as she converted a backhand victor, which drew prolonged applause from the crowd.

Williams played Sunday one day after daughter Olympia's first birthday.

But after compiling 14 winners and only two unforced errors in that set, Williams began making mistakes, becoming less and less comfortable as Kanepi grew increasingly so.

The Estonian missed two break points in the first game of the third set, allowing Williams to fight back and hold serve with a backhand victor, which brought out a loud yell of "come on" from her.

"I feel like it's important for women to know that it doesn't happen like that in the Instagram world". So I have some weapons, too.

"That desire has not gone down at all", she said.

The other quarterfinal on the top half of the draw will be defending champion Sloane Stephens of the USA against No. 19 Anastasija Sevastova of Latvia in a rematch from the same round previous year.

But she said she admired their willingness to use their public profiles to tackle issues of racial and social injustice.

The American struck 17 winners and controlled play from the baseline, ran relentlessly to extend the points, dominated in the longer rallies and was also helped by her opponent's struggles on serve.

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