Expressing measurable functions by one-one ones
نویسندگان
چکیده
منابع مشابه
The Approximation of One-one Measurable Transformations by Measure Preserving Homeomorphisms
This paper contains two results related to the material in [2]. Suppose/is a one-one transformation of the open unit interval /" (where n^2) onto /". 1. If/ is absolutely measureable and £>0, then there is an absolutely measurable homeomorphism ç»t of /" onto /" such that m({x:f(x)^(pc(x) or f~'(x)^ 9'J1W})<£. where m denotes /»-dimensional Lebesgue measure. 2. Suppose p is either (1) a nonatom...
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Let f : R→ R have an nth derivative of finite variation Vf(n) and a locally absolutely continuous (n− 1)st derivative. Denote by E±(f, δ)p the error of onesided approximation of f (from above and below, respectively) by entire functions of exponential type δ > 0 in Lp(R)–norm. For 1 ≤ p ≤ ∞ we show the estimate E±(f, δ)p ≤ C n π1/pVf(n)δ −n− 1 p , with constants Cn > 0.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1982
ISSN: 0001-8708
DOI: 10.1016/0001-8708(82)90020-2