Radon-Nikodym Theorem with Respect to $$(\rho,q)$$-Measure on $$\Bbb Z_p$$

Analogue of Lebesgue-Radon-Nikodym Theorem with respect to p-adic q-Measure on Zp

and Applied Analysis 3 By 2.2 , we get μf,−q ( a pZp ) 2 q 2 qp −qa ∫ Zp f ( a px ) dμ−qpn x . 2.3 Therefore, by 2.3 , we obtain the following theorem. Theorem 2.1. For f, g ∈ C Zp , one has μαf βg,−q αμf,−q βμg,−q, 2.4 where α, β are constants. From 2.2 and 2.4 , we note that ∣μf,−q ( a pZp )∣∣ ≤ M‖f‖∞, 2.5 where ‖f‖∞ supx∈Zp |f x | and M is some positive constant. Now, we recall the definitio...

LEBESQUE-RADON-NIKODYM THEOREM WITH RESPECT TO FERMIONIC p-ADIC INVARIANT MEASURE ON Zp

In this paper we derive the analogue of the Lebesque-Radon-Nikodym theorem with respect to fermionic p-adic invariant measure on Zp. 2010 Mathematics Subject Classification : 11S80, 48B22, 28B99

A Radon-Nikodym approach to measure information

A Reformulation of the Radon-nikodym Theorem

The Radon-Nikodym theorems of Segal and Zaanen are principally concerned with the classification of those measures p. for which any X« p. is given in the form

AN ANALOGUE OF LEBESGUE-RADON-NIKODYM THEOREM WITH RESPECT TO p-ADIC q-INVARIANT DISTRIBUTION ON Zp

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 i...