In Section 4.7 we introduced the space L
(µ) for p ≥ 1 and mentioned that they are Banach spaces. Among these the space L2(µ) has a special role to play in our subject. In fact all statistical problems which centre around ‘extrapolation’ or ‘prediction’ are based on the fundamental properties of the space L2(µ). To elaborate on this theme we shall develop the barest minimum of the theory of Banach and Hilbert spaces.
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