  The main result of this paper is a proof that, for any $f \in L_1[a,b]$, a
sequence of its orthogonal projections $(P_{\Delta_n}(f))$ onto splines of
order $k$ with arbitrary knots $\Delta_n$, converges almost everywhere provided
that the mesh diameter $|\Delta_n|$ tends to zero, namely \[ f \in L_1[a,b]
\Rightarrow P_{\Delta_n}(f,x) \to f(x) \quad \mbox{a.e.} \quad (|\Delta_n|\to
0)\,. \] This extends the earlier result that, for $f \in L_p$, we have
convergence $P_{\Delta_n}(f) \to f$ in the $L_p$-norm for $1 \le p \le
\infty$.}
