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We study the rate of approximation to functions in Lp and, in particular, in Lip(α,p) by weighted means of their Walsh-Fourier series, where α>0 and 1≤p≤∞. For the case p=∞, Lp is interpreted to be CW, the collection of uniformly W continuous functions over the unit interval [0,1). We also note that the weighted mean kernel is quasi-positive, under fairly general conditions.