We then introduce a distance function p which is given in terms of the integral norm || · |li as p(F, 9) := ||f – 9|li Vf,g € C[0, 1] To show that < C[0, 1], p > is a metric space: (a) Prove that the distance function p positive definite on C[0, 1]. (b) Is the distance function p is symmetric? Justify. (c) Show that p satisfies the triangle inequality on C[0, 1].

Q: Please use typefont or legible handwriting with only the necessary steps and clear explanations.

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A: This is a problem of abstract algebra.

Q: sup norm

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