WHITE PLAINS — Bernard B. Kerik, a former New York police commissioner who rose to national prominence, was sentenced to four years inprison on Thursday after pleading guilty to eight felony charges, including tax fraud and lying to White House officials. The sentencing was the end of a legal saga in which federal prosecutors denounced Mr. Kerik, a former detective who rose to the upper echelons of power, as a corrupt official who sought to trade his authority for lavish perks.