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We continue to investigate the notion ofIK${\mathcal I}^{\mathcal K}$   -convergence (which concerns with the convergence with respect to one ideal along a set which is “big” with respect to another ideal) introduced by M. Mačaj and M. Sleziak [ 10 ] with primary focus on sequences of real functions. Our investigation is based on results by R. Filipów and M. Staniszewski [ 5 ,  6 ] or M. Staniszewski [ 11 ].

I K ${\mathcal I}^{\mathcal K}$ -convergence of sequences of functions