A decomposition of bounded, weakly measurable functions
نویسندگان
چکیده
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 کاملWeakly tight functions and their decomposition
The notion of a signed measure arises if a measure is allowed to take on both positive and negative values. A set that is both positive and negative with respect to a signed measure is termed as a null set. Some concepts in measure theory can be generalized by means of classes of null sets. An abstract formulation and proof of the Lebesgue decomposition theorem using the concept of null sets is...
متن کاملDecomposition of threshold functions into bounded fan-in threshold functions
Article history: Received 31 October 2007 Revised 3 March 2011 Available online 10 April 2013
متن کاملMeasurable functions are of bounded variation on a set of dimension 1/2
We show that for every Lebesgue measurable function f : [0, 1] → R there exists a compact set C of Hausdorff dimension 1/2 such that f is of bounded variation on C, and there exist compact sets Cα of Hausdorff dimension 1−α such that f is Hölder-α on Cα (0 < α < 1). These answer questions of M. Elekes, which were open even for continuous functions f . Our proof goes by defining a discrete Hausd...
متن کاملTowers of Measurable Functions
We formulate variants of the cardinals f, p and t in terms of families of measurable functions, in order to examine the effect upon these cardinals of adding one random real.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tatra Mountains Mathematical Publications
سال: 2011
ISSN: 1210-3195
DOI: 10.2478/v10127-011-0025-1