Add to ORKGThis thesis gives a more detailed version of a proof from Daniel Mauldin that the set of continuous functions defined on the interval $[0,1]$ that are nowhere differentiable is not Borel. On the other hand, it is shown that the same set is Lebesgue Measurable. The theorems and definitions that are necessary in the proofs are given in the Glossary, where a knowledge of the course Real Analysis is expected. The proofs of most of these theorems are given in the AppendixElectrical Engineering, Mathematics and Computer ScienceDelft Institute of Applied Mathematic
Abstract. In this note, we prove that the countable compactness of {0, 1} Ê together with the Counta...
summary:In this note, we prove that the countable compactness of $\lbrace 0,1\rbrace ^{{\mathbb{R}}}...
I am going to include in my talk two results emphasizing similarity of Marczewski-measurable sets an...
Let M be the set of all continuous real-valued functions defined on the closed unit interval [0,1] w...
The investigation of computational properties of discontinuous functions is an important concern in ...
AbstractLebesgue proved that every separately continuous function f:R×R→R is a pointwise limit of co...
This paper continues the investigation begun in [M.R. Burke, Topology Appl. 129 (2003) 29-65] into t...
We introduce the new concept of pointwise measurability. It is shown in this paper that a measurable...
Measures and measurable functions are used primarily as tools for carrying out various calculations ...
It is shown that a measurable function from an atomless Loeb probability space (Ω, A, P) to a Polish...
Abstract. The concept of measurability of real-valued functions with re-spect to various classes of ...
AbstractThis paper continues the investigation begun in [M.R. Burke, Topology Appl. 129 (2003) 29–65...
In this paper we present a simple general method for demonstrating that in certain function spaces ...
The author uses the Baire category theorem to prove the existence of nowhere differentiable function...
It is well-known and easy to see that each finite Borel measure on the real line whose null sets con...
Abstract. In this note, we prove that the countable compactness of {0, 1} Ê together with the Counta...
summary:In this note, we prove that the countable compactness of $\lbrace 0,1\rbrace ^{{\mathbb{R}}}...
I am going to include in my talk two results emphasizing similarity of Marczewski-measurable sets an...
Let M be the set of all continuous real-valued functions defined on the closed unit interval [0,1] w...
The investigation of computational properties of discontinuous functions is an important concern in ...
AbstractLebesgue proved that every separately continuous function f:R×R→R is a pointwise limit of co...
This paper continues the investigation begun in [M.R. Burke, Topology Appl. 129 (2003) 29-65] into t...
We introduce the new concept of pointwise measurability. It is shown in this paper that a measurable...
Measures and measurable functions are used primarily as tools for carrying out various calculations ...
It is shown that a measurable function from an atomless Loeb probability space (Ω, A, P) to a Polish...
Abstract. The concept of measurability of real-valued functions with re-spect to various classes of ...
AbstractThis paper continues the investigation begun in [M.R. Burke, Topology Appl. 129 (2003) 29–65...
In this paper we present a simple general method for demonstrating that in certain function spaces ...
The author uses the Baire category theorem to prove the existence of nowhere differentiable function...
It is well-known and easy to see that each finite Borel measure on the real line whose null sets con...
Abstract. In this note, we prove that the countable compactness of {0, 1} Ê together with the Counta...
summary:In this note, we prove that the countable compactness of $\lbrace 0,1\rbrace ^{{\mathbb{R}}}...
I am going to include in my talk two results emphasizing similarity of Marczewski-measurable sets an...