…The median apartment rent in Brooklyn, the most populous of New York’s five boroughs and once a refuge from Manhattan’s sky-high costs, was the highest in at least five years in August, rising 4.6 percent from a year earlier to $2,850, according to appraiser Miller Samuel Inc. and broker Douglas Elliman Real Estate….

…The median price of a new-development condominium in Brooklyn was $704,918 in the second quarter, about 50 percent of the median in Manhattan, according to Miller Samuel and Douglas Elliman….

…Renting an apartment in North Brooklyn in the second quarter was 22 percent cheaper on average than renting in Manhattan, according to data compiled by Miller Samuel….

…“The perception that you can get more for your money in Brooklyn is being challenged,” said Jonathan Miller, president of Miller Samuel….