Wyniki wyszukiwania

1

Continuous-, derivative-, and differentiable-restrictions of measurable functions

100%

Brown J. B.

Fundamenta Mathematicae

|

1992

|

tom 141

|

nr 1

85-95

EN

We review the known facts and establish some new results concerning continuous-restrictions, derivative-restrictions, and differentiable-restrictions of Lebesgue measurable, universally measurable, and Marczewski measurable functions, as well as functions which have the Baire properties in the wide and restricted senses. We also discuss some known examples and present a number of new examples to show that the theorems are sharp.

2

Marczewski-Burstin-like characterizations of σ-algebras, ideals, and measurable functions

64%

Brown J. B., Elalaoui-Talibi H.

Colloquium Mathematicum

|

1999

|

tom 82

|

nr 2

277-286

EN

ℒ denotes the Lebesgue measurable subsets of ℝ and $ℒ_0$ denotes the sets of Lebesgue measure 0. In 1914 Burstin showed that a set M ⊆ ℝ belongs to ℒ if and only if every perfect P ∈ ℒ\$ℒ_0$ has a perfect subset Q ∈ ℒ\$ℒ_0$ which is a subset of or misses M (a similar statement omitting "is a subset of or" characterizes $ℒ_0$). In 1935, Marczewski used similar language to define the σ-algebra (s) which we now call the "Marczewski measurable sets" and the σ-ideal $(s^0)$ which we call the "Marczewski null sets". M ∈ (s) if every perfect set P has a perfect subset Q which is a subset of or misses M. M ∈ $(s^0)$ if every perfect set P has a perfect subset Q which misses M. In this paper, it is shown that there is a collection G of $G_δ$ sets which can be used to give similar "Marczewski-Burstin-like" characterizations of the collections $B_w$ (sets with the Baire property in the wide sense) and FC (first category sets). It is shown that no collection of $F_σ$ sets can be used for this purpose. It is then shown that no collection of Borel sets can be used in a similar way to provide Marczewski-Burstin-like characterizations of $B_r$ (sets with the Baire property in the restricted sense) and AFC (always first category sets). The same is true for U (universally measurable sets) and $U_0$ (universal null sets). Marczewski-Burstin-like characterizations of the classes of measurable functions are also discussed.

3

Almost continuous Darboux functions and Reed's pointwise convergence criteria

50%

Brown J. B.

Fundamenta Mathematicae

|

1974-1975

|

tom 86

|

nr 1

1-7

4

Lusin density and Ceder's differentiable restrictions of arbitrary real functions

50%

Brown J. B.

Fundamenta Mathematicae

|

1974

|

tom 84

|

nr 1

35-45

5

Metric spaces in which a strengthened form of Blumberg's theorem holds

44%

Brown J. B.

Fundamenta Mathematicae

|

1971

|

tom 71

|

nr 3

243-253

6

On the Baire order of concentrated spaces and $L_1$ spaces

44%

Brown J. B.

Fundamenta Mathematicae

|

1977

|

tom 94

|

nr 2

165-172

7

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On the relationship between Menger spaces and Wald spaces

44%

Brown J. B.

Colloquium Mathematicum

|

1973

|

tom 27

|

nr 2

323-330

8

Baire category in spaces of probability measures

38%

Brown J. B.

Fundamenta Mathematicae

|

1977

|

tom 96

|

nr 3

189-193

9

Totally discontinuous connectivity functions

38%

Brown J. B.

Colloquium Mathematicum

|

1971

|

tom 23

|

nr 1

53-60

10

The Ramsey sets and related sigma algebras and ideals

38%

Brown J. B.

Fundamenta Mathematicae

|

1990

|

tom 136

|

nr 3

179-185

11

Nowhere dense Darboux graphs

32%

Brown J. B.

Colloquium Mathematicum

|

1969

|

tom 20

|

nr 2

243-247

Ograniczanie wyników

7 Fundamenta Mathematicae

4 Colloquium Mathematicum

11 Brown J. B.

1 Elalaoui-Talibi H.

1 1999

1 1992

1 1990

2 1977

2 1974

1 1973

2 1971

1 1969

Continuous-, derivative-, and differentiable-restrictions of measurable functions

Marczewski-Burstin-like characterizations of σ-algebras, ideals, and measurable functions

Almost continuous Darboux functions and Reed's pointwise convergence criteria

Lusin density and Ceder's differentiable restrictions of arbitrary real functions

Metric spaces in which a strengthened form of Blumberg's theorem holds

On the Baire order of concentrated spaces and $L_1$ spaces

On the relationship between Menger spaces and Wald spaces

Baire category in spaces of probability measures

Totally discontinuous connectivity functions

The Ramsey sets and related sigma algebras and ideals

Nowhere dense Darboux graphs