An Inequality for Correlated Measurable Functions

نویسندگان

  • FABIO ZUCCA
  • S. Abramovich
چکیده

A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We give two applications of this result, one of them to a problem arising from probability theory.

برای دانلود رایگان 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

Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

متن کامل

An inequality related to $eta$-convex functions (II)

Using the notion of eta-convex functions as generalization of convex functions, we estimate the difference between the middle and right terms in Hermite-Hadamard-Fejer inequality for differentiable mappings. Also as an application we give an error estimate for midpoint formula.

متن کامل

Inequalities of Ando's Type for $n$-convex Functions

By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.

متن کامل

Notes on L(Ω,M, μ) and the Riesz–Fischer Theorem

Let (Ω, M, µ) be a measure space. Then for any two complex valued measurable functions f and g, we have the Cauchy-Schwarz inequality: 0.1 THEOREM (Cauchy-Schwarz inequality). Let (Ω, M, µ) be a measure space. Then for any two complex valued measurable functions f and g such that

متن کامل

Non-commutative Jensen and Chebyshev inequalities for measurable matrix-valued functions and measures

The idea of noncommutative averaging (that is, of a matrix-convex combination of matrixvalued functions) extends quite naturally to the integral of matrix-valued measurable functions with respect to positive matrix-valued measures. In this lecture I will report on collaborative work with F. Zhou, S. Plosker, and M. Kozdron on formulations of some classical integral inequalities (Jensen, Chebysh...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008