Marczewski sets, measure and the Baire property
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...
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
Measurability of functions with values in partially ordered spaces
Measurability of multifunctions of two variables [Book]
Measurability of real functions defined on the product of metric spaces
Measurable Functions and Almost Continuous Functions.
Measurable relations
Measurable Selection Theorems for Optimization Problems.
Measurable solutions of functional equations satisfied almost everywhere.
Measurable uniform spaces
Measure and measurable functions of
Mengenwertige Masse und Fortsetzungen.
Monotone approximation of measurable multifunctions by simple multifunctions
We investigate the problem of approximation of measurable multifunctions by monotone sequences of measurable simple ones. Our main tool is the Marczewski function, i.e., the characteristic function of a sequence of sets.
Multifractal analysis of a class of additive processes with correlated non-stationary increments.
Multifractals and projections.
In this paper, we generalize the result of Hunt and Kaloshin [5] about the Lq-spectral dimensions of a measure and that of its projections. The results we obtain, allow to study an untreated case in their work and to find a relationship between the multifractal spectrum of a measure and that of its projections.