And Still One More Proof of the Radon-Nikodym Theorem

نویسنده

  • Anton R. Schep
چکیده

1. J. Burbea, Sharp inequalities for holomorphic functions, Illinois J. Math. 31 (1987) 248–264. 2. T. Carleman, Zur Theorie der Minimalflächen, Math. Z. 9 (1921) 154–160. 3. P. L. Duren, Theory of H p Spaces, Academic Press, New York, 1970; reprinted by Dover, Mineola, NY, 2000. 4. T. W. Gamelin and D. Khavinson, The isoperimetric inequality and rational approximation, this MONTHLY 96 (1989) 18–30. 5. G. H. Hardy and J.E. Littlewood, Some properties of fractional integrals, II, Math. Z. 34 (1932) 403–439. 6. H. Hedenmalm, B. Korenblum, and K. Zhu, Theory of Bergman Spaces, Springer-Verlag, New York, 2000. 7. M. Mateljević and M. Pavlović, New proofs of the isoperimetric inequality and some generalizations, J. Math. Anal. Appl. 98 (1984) 25–30.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A new proof for the Banach-Zarecki theorem: A light on integrability and continuity

To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

متن کامل

Differentiability of Lipschitz Maps from Metric Measure Spaces to Banach Spaces with the Radon Nikodym Property

In this paper we prove the differentiability of Lipschitz maps X → V , where X is a complete metric measure space satisfying a doubling condition and a Poincaré inequality, and V denotes a Banach space with the Radon Nikodym Property (RNP). The proof depends on a new characterization of the differentiable structure on such metric measure spaces, in terms of directional derivatives in the direct...

متن کامل

The Radon-Nikodym problem for approximately proper equivalence relations

We study the Radon-Nikodym problem for approximately proper equivalence relations and more specifically the uniqueness of certain Gibbs states. One of our tools is a variant of the dimension group introduced in the study of AF algebras. As applications, we retrieve sufficient conditions for the uniqueness of traces on AF algebras and parts of the PerronFrobenius-Ruelle theorem.

متن کامل

A Radon-Nikodym derivative for almost subadditive set functions

In classical measure theory, the Radon-Nikodym theorem states in a concise condition, namely domination, how a measure can be factorized by another (bounded) measure through a density function. Several approaches have been undertaken to see under which conditions an exact factorization can be obtained with set functions that are not σ-additive (for instance finitely additive set functions or su...

متن کامل

Information-Theoretic Demensionality Reduction for Poisson Models: Supplementary Material

Proof of Theorem 1. We first establish the following Lemma. Lemma 1. Consider random variables X ∈ R and Y ∈ R. Let f Y |X be the Radon-Nikodym derivatives of probability measure P θ Y |X with respect to arbitrary measures QY provided that P θ Y |X QY . θ ∈ R is a parameter. f Y is the Radon-Nikodym derivatives of probability measure P θ Y with respect to QY provided that P θ Y QY . Note that i...

متن کامل

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

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • The American Mathematical Monthly

دوره 110  شماره 

صفحات  -

تاریخ انتشار 2003