Placeholder: While bulk of the literature is on SA for the case when the observations are from a finite dimensional Euclidian space, there has been interest in extending the same to infinite dimen-sion. Extension to Hilbert spaces is relatively easier to do, but this is not so when we come to a Banach space - since in the case of a Banach space, even law of large numbers is not true in general. We consider some cases where approximation works in a Banach space. Our framework includes case when the Banach spa While bulk of the literature is on SA for the case when the observations are from a finite dimensional Euclidian space, there has been interest in extending the same to infinite dimen-sion. Extension to Hilbert spaces is relatively easier to do, but this is not so when we come to a Banach space - since in the case of a Banach space, even law of large numbers is not true in general. We consider some cases where approximation works in a Banach space. Our framework includes case when the Banach spa

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While bulk of the literature is on SA for the case when the observations are from a finite dimensional Euclidian space, there has been interest in extending the same to infinite dimen-sion. Extension to Hilbert spaces is relatively easier to do, but this is not so when we come to a Banach space - since in the case of a Banach space, even law of large numbers is not true in general. We consider some cases where approximation works in a Banach space. Our framework includes case when the Banach spa

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