On the Baire order of concentrated spaces and spaces
Lusin density and Ceder's differentiable restrictions of arbitrary real functions
The Ramsey sets and related sigma algebras and ideals
Continuous-, derivative-, and differentiable-restrictions of measurable functions
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.
Baire category in spaces of probability measures
Metric spaces in which a strengthened form of Blumberg's theorem holds
Almost continuous Darboux functions and Reed's pointwise convergence criteria
Marczewski-Burstin-like characterizations of σ-algebras, ideals, and measurable functions
ℒ denotes the Lebesgue measurable subsets of ℝ and 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$ℒ0 which is a subset of or misses M (a similar statement omitting “is a subset of or” characterizes ). In 1935, Marczewski used similar language to define the σ-algebra (s) which we now call the “Marczewski measurable sets” and the σ-ideal which we call the “Marczewski null sets”. M ∈ (s) if every perfect set P has...
Totally discontinuous connectivity functions
Nowhere dense Darboux graphs
On the relationship between Menger spaces and Wald spaces
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