Real Analysis Exchange

Recursive set relations.

H. Fast, H. Fejzić, C. Freiling, and D. Rinne

Full-text: Open access

Abstract

Let $A(x)$, $B(x)$, $C(x)$ be characteristic functions of three measurable sets of real numbers. We determine necessary and sufficient conditions for which $A(x+a_{n})+B(x+b_{n})+C(x+c_{n})=A(x)+B(x)+C(x)$ almost everywhere, where $\{ a_n\},\{ b_n\},\{ c_n\}$ are sequences of nonzero shifts approaching zero.

Article information

Source
Real Anal. Exchange Volume 29, Number 2 (2003), 835- 851.

Dates
First available in Project Euclid: 7 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149698546

Mathematical Reviews number (MathSciNet)
MR2083818

Subjects
Primary: 26A12: Rate of growth of functions, orders of infinity, slowly varying functions [See also 26A48]

Keywords
recursion periodic sets shift invariance

Citation

Fast, H.; Fejzić, H.; Freiling, C.; Rinne, D. Recursive set relations. Real Anal. Exchange 29 (2003), no. 2, 835-- 851.https://projecteuclid.org/euclid.rae/1149698546


Export citation

References

  • W. Rudin, Real and Complex Analysis, 3rd ed. McGraw-Hill, New York, 1986.