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Disclosed is a catalyst carrier (10) which is obtained by mixing rare earth element oxide fine particles (ceria particles (11)) composed of primary particles of a rare earth element oxide, alumina fine particles (12) composed of primary particles of alumina, and barium compound fine particles (13) composed of primary particles of a barium compound. The rare earth element oxide fine particles have a primary particle diameter of not more than 5 nm, and the barium compound fine particles (13) have a primary particle diameter of not more than 10 nm. Platinum fine particles (20) are substantially supported by the rare earth element oxide fine particles in this catalyst carrier (10). Consequently, particle growth of platinum as an oxidation catalyst and particle growth of barium as a NOx absorbent can be surely suppressed.