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We postpone to another occasion the proof of THEOREM 7. Let the function f(x) be of class CO on a closed bounded interval E, and let pn(x) (0 f (x) on E) be a polynomial of degree n which for some p, 0 < p < 1, minimizes (3). Let f(x) pn(X) have zeros of respective inultiplicities Kj, 1 < j < r, and let Kj* be the smallest integer > f(1p) Kj] and which for zeros interior to E is also of the same parity as Kp. Then we have

NOTE ON INVARIANCE OF DEGREE OF POLYNOMIAL AND TRIGONOMETRIC APPROXIMATION UNDER CHANGE OF INDEPENDENT VARIABLE