AN ANALOGUE OF LEBESGUE-RADON-NIKODYM THEOREM WITH RESPECT TO p-ADIC q-INVARIANT DISTRIBUTION ON Zp
نویسندگان
چکیده
Let p be a fixed prime. Throughout this paper Z, Zp, Qp, and Cp will, respectively, denote the ring of rational integers, the ring of p-adic rational integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp, cf.[1, 2, 3]. Let vp be the normalized exponential valuation of Cp with |p| = p −vp(p) = p and let a+ pZp = {x ∈ Zp|x ≡ a( mod p N )}, where a ∈ Z lies in 0 ≤ a < p . In this paper we assume that q ∈ Cp with |1 − q| < p − 1 p−1 as an indeterminate. We now use the notation [x]q = [x : q] = 1− q 1− q , cf. [1, 2, 3].
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