When will the sample paths be step functions for two-parameter stochastic processes (Q689495)

The authors consider complete separable two-parameter stochastic processes \(X(s,t)\), \((s,t) \in[a,b] \times[c,d]\) (in other words, such a process has limits in all quadrants \(Q^{\pm \pm}_{(s,t)})\). The main result is: if there exists such a constant \(K\) that \[ \sum^ n_{i=1}P \{\Delta^ 1x(a_ i,c) \neq 0\}+\sum^ n_{j=1}P \{ \Delta^ 2x(a,b_ j) \neq 0\}+ \sum^ n_{i,j=1} P\{X](a_{i-1},b_{j-1}),\;(a_ i,b_ j)] \neq 0\} \leq K, \] then the sample paths of \(X\) are step functions with probability 1.