BOSTON – Justices of the state Supreme Judicial Court, in a decision released Tuesday, denied a request for a new trial by a Lynn man convicted of the May 2005 murders of a father and his 16-year-old daughter inside their 58 Cottage St. apartment.Pytou Heang, 31, formerly of 158 Lawton Ave., Lynn, was one of three men convicted in the murders of Robert A. Finnerty Sr., 47, and Amy Dumas, 16.Heang was convicted by a Superior Court jury in Lawrence in June 2008 of two counts of first-degree murder, armed home invasion and other firearms charges. He is serving two consecutive life sentences in prison without the possibility of parole.Phap Buth, 35, was convicted in a separate trial that same month of two counts of first-degree murder and home invasion and is also serving two life sentences.Chon Son, 24, formerly of 591 Lincoln Ave., Saugus, pleaded guilty to two counts of second-degree murder and home invasion charges and is serving life in prison with possibility of parole after 27 years.The trio, on May 16, 2005, forced their way into the victims’ apartment where they had visited earlier in the evening to purchase marijuana.Finnerty, who was seated and used the assistance of a walker, was shot in the chest. When Dumas intervened to try and save her father, she was shot in the back.Heang appealed his conviction and requested a new trial, alleging the trial judge, Richard E. Welch III, improperly admitted evidence at trial, including expert testimony on ballistics, statements he made to police, statements made by one of his co-defendants and videotape surveillance footage from a store.Heang also challenged the judge’s questioning of prospective jurors and finally alleged evidence presented at trial did not support the jury’s verdict.The high court found no basis for Heang’s appeal.The appeal was reviewed by Chief Justice Roderick Ireland and Justices Francis Spina, Margo Botsford and Ralph Gants.”We conclude that the judge’s rulings were either not error or not prejudicial error and the evidence was sufficient to sustain the convictions,” the Justices wrote. “Accordingly, we affirm the defendant’s convictions. After a complete review of the record, we also conclude there is no basis to exercise our power to reduce his murder convictions to a lesser degree of guilt or to order a new trial.