The object of this note in to show that various commonly used measures of decree of approximation are invariant under one-to-one analytic transformation of the independent variable, and this is true for both approximation by polynomials in the complex variable and trigonometric approximation in the real variable. The methods used here have already been used several times in the literature, especially by J.H. Curtiss, and Walsh and Sewell, and Walsh, but the present treatment is more unified and core complete, and emphasizes for the first tine invariance of degrees of approximation.
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