Mappings of finite distortion: composition operator.
Marczewski sets in the Hashimoto topologies for measure and category
Marczewski sets, measure and the Baire property
Marczewski-Burstin Representations of Boolean Algebras Isomorphic to a Power Set
The paper contains some sufficient conditions for Marczewski-Burstin representability of an algebra 𝓐 of sets which is isomorphic to 𝓟(X) for some X. We characterize those algebras of sets which are inner MB-representable and isomorphic to a power set. We consider connections between inner MB-representability and hull property of an algebra isomorphic to 𝓟 (X) and completeness of an associated quotient algebra. An example of an infinite universally MB-representable algebra is given.
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...
Martin's axiom and medial functions.
Maximally conjugate sigma-algebras represented as hypergraphs
Measurability of equivalence classes and MEC-property in metric spaces.
Measurability of Functions of Two Variables
Measurability of functions with approximately continuous vertical sections and measurable horizontal sections
Measurable cardinals and category bases
We show that the existence of a non-trivial category base on a set of regular cardinality with each subset being Baire is equiconsistent to the existence of a measurable cardinal.
Measurable spaces with c.c.c. [Book]
Measurable uniform spaces
Measure and category versions of Erdős-Rado theorem.
Measure-additive coverings and measurable selectors [Book]
Measure-theoretic unfriendly colorings
We consider the problem of finding a measurable unfriendly partition of the vertex set of a locally finite Borel graph on standard probability space. After isolating a sufficient condition for the existence of such a partition, we show how it settles the dynamical analog of the problem (up to weak equivalence) for graphs induced by free, measure-preserving actions of groups with designated finite generating set. As a corollary, we obtain the existence of translation-invariant random unfriendly colorings...
Mesurable Outer Kernels Of Sets
Metric properties of some planar sets
Minimal complementation and maximal conjugation for partitions, with an application to Blackwell sets
Mixtures of non-atomic measures, II