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The fiercest congressional contest was in the 6th District, on Boston’s North Shore, where Tisei was trying to unseat Tierney, an eight-term Democrat. Tierney’s wife, Patrice, had been sentenced to 30 days in prison last year for helping one of her two brothers who had been implicated in the gambling ring file false tax returns.

Tierney claimed victory early Wednesday, but Tisei initially refused to concede and his campaign said it was examining possible voting irregularities. The Republican conceded the race later in the day, while saying he still had concerns about possible voting problems in the district.

Kennedy was the first member of his famous political family to seek public office. A former prosecutor, he tapped into his family’s name and connections to raise more than $4 million for the race and will take the seat now held by the retiring Democratic Rep. Barney Frank in the district stretching from the western Boston suburbs to southeastern Massachusetts.

Democratic incumbents carried the day in the state’s other House races.

Rep. Edward Markey, the dean of the state’s congressional delegation, defeated Republican Tom Tierney in the 5th district; Rep. Niki Tsongas bested Jon Golnick in the 3rd district; freshman Rep. William Keating defeated Christopher Sheldon in the 9th district; Rep. Stephen Lynch won over Republican Joe Selvaggi in the 8th district; and Rep. Michael Capuano won over independent Karla Romero in the 7th District.

Rep. Richard Neal in the 1st District and Rep. James McGovern in the 2nd District were unopposed Tuesday.