NUMBER-SYSTEMS AND REPARTITION

[摘要] Given a number system T = (0, 1), T(j), (J(n, j)n is-an-element-of E(j))j greater-than-or-equal-to 0, we define a measurable mapping PHI(T): (0, 1)N --> (0, 1) such that lambda(infinity) (PHI(T)-1(A)) = lambda(A), A is-an-element-of B(0, 1). A measurable section (t(n)(.))n greater-than-or-equal-to 0 is defined for PHI(T); t(n)(.) has uniform distribution for any n greater-than-or-equal-to 0. Conditions relative to lambda-a.e. repartition properties of (t(n)(.))n greater-than-or-equal-to 0 are studied. Applications to (alpha, gamma)-expansions, Cantor products, and continued fractions are given. (C) 1994 Academic Press, Inc.

[发布日期] 1994-12-01