Theorem 2 and later results including the corollaries have application to the dual problem, approximation by functions of type RAn(z) considered in reference 3. The methods of the present note for the study of convergence and degree of convergence on subsets of Ep apply when the number of free poles of the approximating rational functions is finite, and by dualization apply when the number of their free zeros is finite; they do not apply when the number of both free poles and zeros is infinite.
Some obscure, yet fundamental, formulae of integral geometry are re-considered. They are applied to determine all the moments of the random volume of various isotropic random r-dimensional simplices in En (r = 1, …, n).
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