A linear functional T on a Frechet algebra (A, (p_n)) is called almost multiplicative with respect to the sequence (pn), if there exists " epsilon >=0 such that |Tab − TaTb| <= p_n((a))p_n((b)) for all n in N and for every a, b in A. We show that an almost multiplicative linear functional on a Frechet algebra is either multiplicative or it is continuous, and hence every almost multiplicative linear functional on a functionally continuous Frechet algebra is continuous.
