a bearing including an outer member having an inner peripheral surface formed with a plurality of circumferentially extending raceway surfaces, an inner member having a center bore defined therein and also having an outer peripheral surface formed with circumferentially extending raceway surfaces in alignment with the raceway surfaces in the outer member, and rows of rolling elements operatively interposed between the raceway surfaces in the outer member and the raceway surfaces in the inner member, respectively, the center bore of the inner member receiving and fixing therein a stem formed in an outer race of a constant velocity universal joint;

a rotation sensor assembly including an encoder, mounted on one end of the inner member, and a rotation sensor mounted on one end of the outer member in face-to-face relation with the encoder, the encoder including a core metal press-fitted onto the one end of the inner member and having a cylindrical wall and a cylindrical extension, the cylindrical extension extending axially outwardly from one end of the cylindrical wall beyond an end face of the inner member; and

a displacement sensor assembly including a pair of displacement sensors mounted on the one end of the outer member that is in face-to-face relation with the cylindrical extension, the displacement sensors being equidistantly spaced from each other in a circumferential direction and detecting a radial distance between the displacement sensor and the cylindrical extension, the rotation sensor being disposed between the displacement sensors in the circumferential direction.