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We prove ergodicity of a class of infinite measure preserving systems, called skew-products. More precisely, we consider systems of the form \ Tf: [0, 1) R[0, 1) R, Tf (x, t): = (T (x), t+f (x) ), \ where T is an interval exchange transformation and f is a piece-wise constant function with a finite number of discontinuities. We show that such system is ergodic with respect to Leb[₀, ₁) ₑ for a typical choice of parameters of T and f.
Argentieri et al. (Mon,) studied this question.