Diurnal and nocturnal trunk and limb motor activity of 20 healthy individuals was evaluated by actimetry for 45 consecutive hours. Sleep was assessed by sleep logs. Overall, motor activity significantly (p < .05) decreased in the order wrist, ankle, and trunk. There was significantly more motor activity in the dominant wrist during the diurnal period. Motor activity was significantly affected by the 24-hr sleep-wake cycle, with lower levels and prolonged immobility during the night. Time series analyses revealed different but significant correlations between motor activity at all sites. These data imply that (a) motor activity should be recorded at the dominant wrist when the highest level of motor activity is of importance, (b) recordings at the nondominant wrist are better indicators of trunk movement than are dominant wrist recordings, and (c) sites other than the conventional nondominant wrist recording site should be evaluated to improve the validity of motor activity-based sleep-wake scoring.

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Let O be a p-adic field of characteristic zero and let G be a connected, reductive, linear algebraic group, defined over O. Denote by G the group of O-rational points of G. We call G a reductive p-adic group. G is locally compact, separable and unimodular. Keeping to the notation of [2], let (P, A) be a parabolic pair in G with corresponding Levi decomposition P = M N . Let Z be a unitary character of A. Denote by 0 a supercuspidal x-representation of M. It is known (cf. [2]) that the character of Q exists (as a distribution) and is actually given by a locally integrable function on M which is locally constant on the set of regular elements M ' of M; moreover the character is completely determined by its values on the regular elliptic set M e of M. Extend 0 to P by Q(mn) = o(m)(m ~ M, n ~ N).Then Q is a unitary representation of P. Let n = ind Q, the unitary represenPrG tation of G induced by Q in the sense of Mackey. Then we shall show that the character of n is a distribution given by a locally integrable function on G which is locally constant on the regular set G'. If the character of Q is known, the function can be given in detail. As a consequence we derive a necessary and sufficient condition in order that two of the above induced representations are equivalent (Theorem 4).The contents of this paper is inspired by [1] 1 . Throughout this paper, we keep to the notations and terminology of [2]. § 2. Preliminary Results on IntegrationThe contents of this paragraph is elementary. The reader who wants to take Jacobi's substitution theorem for integrals for granted, will probably skip this paragraph.Let O be a p-adic field, i.e. a locally compact field with a non-trivial discrete valuation. In this paragraph we do not assume that char O = 0. Fix an additive Haar measure on O and take on O" the product measure.1 In case ~ is the field of the real numbers and G is a connected semisimple Lie group with finite centre, a detailed study of the induced representations has recently been made by R. L. Lipsman, J. Math. Soc. Japan, vol 23, 3, 452-480 (1971).

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