令f(x)=o(x^m),g(x)=o(x^n),即有lim f(x)/x^m=0,lim g(x)/x^n=0,于是lim f(x)*g(x)/x^(m+n)=lim f(x)/x^m *lim g(x)/x^n=0,即f(x)*g(x)=o(x^(m+n)),于是o(x^m)*o(x^n)=o(x^(m+n)).