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In the absence of the two other men vying for the title of the greatest male player of the modern era, Roger Federer and Rafa Nadal, Djokovic is an odds-on favourite with the bookmakers to win a fourth US Open crown.
The female official faced a backlash from fans of the world No. 1 on social media.
Rublev, 23, had previously won tournaments in Doha, Adelaide, Hamburg and St Petersburg and improved to a Tour-leading 39 wins in 2020 -- tied with world No. 1 Djokovic.
Medvedev's 6-3, 6-4 win over Zverev put him joint top of the Tokyo Group alongside world No. 1 Djokovic, who put on a masterclass to trounce debutant Schwartzman 6-3, 6-2.
Federer, who got involved in a lengthy argument with the chair umpire during the ill-tempered third set, converted his first match point and will meet Novak Djokovic for a place in Sunday's final.
Rafael Nadal and Novak Djokovic kickstarted their build-up to the Australian Open with straight-sets wins at the ATP Cup Saturday, but world number four Dominic Thiem slumped to defeat.
It was Djokovic's fifth victory over the 20-year-old Canadian in as many clashes but by far the toughest, after Shapovalov controlled significant portions of the match played in Australia's intense summer heat.
The world's top players have assembled for the ATP Cup and are using the event to prepare for the year's first Grand Slam, which starts in Melbourne from January 20.
After recent bushfire smog largely cleared in Melbourne, the view is all too familiar with Djokovic and Serena, who is seeking a record-equalling 24th Major title, installed as the bookies' favourites.
Rafael Nadal secured a come-back victory against Australia's Alex De Minaur at the ATP Cup, propelling Spain into the final of the inaugural event.
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