Examples of ε-exhaustive pathological submeasures
For any given ε > 0 we construct an ε-exhaustive normalized pathological submeasure. To this end we use potentially exhaustive submeasures and barriers of finite subsets of ℕ.
Exceptional directions for Sierpiński's nonmeasurable sets
In [2] the question was considered in how many directions can a nonmeasurable plane set behave even "better" than the classical one constructed by Sierpiński in [6], in the sense that any line in a given direction intersects the set in at most one point. We considerably improve these results and give a much sharper estimate for the size of the sets of those "better" directions.
Exceptional sets with respect to Lebesgue differentiation of functions in Sobolev spaces
Existence and integral representation of regular extensions of measures
Let ℒ be a δ-lattice in a set X, and let ν be a measure on a sub-σ-algebra of σ(ℒ). It is shown that ν extends to an ℒ-regular measure on σ(ℒ) provided ν*|ℒ is σ-smooth at ∅ and ν*(L) = inf ν*(U)|X ∖ U ∈ ℒ, Usupset L for all L ∈ ℒ. Moreover, a Choquet type representation theorem is proved for the set of all such extensions.
Existence and properties of -sets.
Existence and uniqueness of diffusions on finitely ramified self-similar fractals
Existence et régularité höldérienne des fonctions de bosses
We discuss the almost sure existence of random functions that can be written as sums of elementary pulses. We then estimate their uniform Hölder regularity by applying some results on coverings by random intervals.
Existence of equilibria in finitely additive nonatomic coalition production economies.
Existence of invariant measures for piecewise continuous transformations
Existence of non measurable sets
Extending Coarse-Grained Measures
In [4] it is proved that a measure on a finite coarse-grained space extends, as a signed measure, over the entire power algebra. In [7] this result is reproved and further improved. Both the articles [4] and [7] use the proof techniques of linear spaces (i.e. they use multiplication by real scalars). In this note we show that all the results cited above can be relatively easily obtained by the Horn-Tarski extension technique in a purely combinatorial manner. We also characterize the pure measures...
Extending Minimal Varieties.
Extending quasi-invariant measures by using subgroups of a given group.
Extension and regularity of -group valued measures
Extensión de medidas difusas usando la esperanza monótona.
The monotone expectation is defined as a functional over fuzzy measures on finite sets. The functional is based on Choquet functional over capacities and its more relevant properties are proved, including the generalization of classical mathematical expectation and Dempster's upper and lower expectations of an evidence. In second place, the monotone expectation is used to define measures of fuzzy sets. Such measures are compared with the ones based on Sugeno integral. Finally, we prove a generalization...
Extension of a valuation on a lattice
Extension of Linear Operators
Extension of measure-like set functions
Extension of measures: a categorical approach
We present a categorical approach to the extension of probabilities, i.e. normed -additive measures. J. Novák showed that each bounded -additive measure on a ring of sets is sequentially continuous and pointed out the topological aspects of the extension of such measures on over the generated -ring : it is of a similar nature as the extension of bounded continuous functions on a completely regular topological space over its Čech-Stone compactification (or as the extension of continuous...
Extension of measures and integrals by the help of a pseudometric