The Democrat, Representative Kyrsten Sinema, initially trailed the Republican, Representative Martha McSally. But as more mail ballots were counted, Ms. Sinema jumped into the lead. Her vote share kept growing until the Associated Press declared her the winner on Monday. A recount would have been triggered if the final margin between the candidates was less than or equal to one-tenth of 1 percent, but this is now unlikely because of the size of Ms. Sinema’s lead.