Cauchy condition for the convergence in category

It is well known that the sequence $\{f_n\}_{n\in N}$ of real measurable functions converges in measure to some measurable function $f$ if and only if $\{f_n\}_{n\in N}$ is fundamental in measure. In this note we introduce the notion of sequence fundamental in category in this manner such that the sequence $\{f_n\}_{n\in N}$ of real functions having the Baire property converges in category to some function $f$ having the Baire property if and only if $\{f_n\}_{n\in N}$ is fundamental in category.