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Abstract In this paper, the idea of lacunary I λ $I_{\lambda}$ -statistical convergent sequence spaces is discussed which is defined by a Musielak-Orlicz function. We study relations between lacunary I λ $I_{\lambda}$ -statistical convergence with lacunary I λ $I_{\lambda}$ -summable sequences. Moreover, we study the I λ $I_{\lambda}$ -lacunary statistical convergence in probabilistic normed space and discuss some topological properties.