Estabilidad de la convergencia débil de medidas.
Estimates for capacities and traces of potentials.
Estimates of capacity of self-similar measures
We give lower and upper estimates of the capacity of self-similar measures generated by iterated function systems where are bi-lipschitzean transformations.
Estimates of L p norms for sums of positive functions
We present new inequalities of Lp norms for sums of positive functions. These inequalities are useful for investigation of convergence of simple partial fractions in Lp(ℝ).
Estimating mathematical information on Graphs: A Scientific Approach
Estimations de la dimension inférieure et de la dimension supérieure des mesures
Étude de certains processus (stochastiquement) différentiables ou holomorphes
Etude spectrale des substitutions de longueur constante
Eulersche Charakteristik, Projektionen und Quermaßintegrale.
Evaluation formulas for a conditional Feynman integral over Wiener paths in abstract Wiener space
In this paper, we introduce a simple formula for conditional Wiener integrals over , the space of abstract Wiener space valued continuous functions. Using this formula, we establish various formulas for a conditional Wiener integral and a conditional Feynman integral of functionals on in certain classes which correspond to the classes of functionals on the classical Wiener space introduced by Cameron and Storvick. We also evaluate the conditional Wiener integral and conditional Feynman integral...
Evaluations of fuzzy sets based on orderings and measures.
Total orderings in the range of fuzzy sets can serve as choice criteria for fuzzy sets, a wide class of orderings based on functions is proposed (section 2). Decomposable measures are taken to measure the items on which the fuzzy sets are given (section 3). Combining the two levels of measurement by means of the integral introduced by the second author we obtain evaluations of fuzzy sets as functionals with appropriate properties, the concepts of energy and fuzziness are included (section 4).
Events of Borel Sets, Construction of Borel Sets and Random Variables for Stochastic Finance
We consider special events of Borel sets with the aim to prove, that the set of the irrational numbers is an event of the Borel sets. The set of the natural numbers, the set of the integer numbers and the set of the rational numbers are countable, so we can use the literature [10] (pp. 78-81) as a basis for the similar construction of the proof. Next we prove, that different sets can construct the Borel sets [16] (pp. 9-10). Literature [16] (pp. 9-10) and [11] (pp. 11-12) gives an overview, that...
Every Lusin set is undetermined in the point-open game
We show that some classes of small sets are topological versions of some combinatorial properties. We also give a characterization of spaces for which White has a winning strategy in the point-open game. We show that every Lusin set is undetermined, which solves a problem of Galvin.
Exactness of expanding mappings
Examples of non-shy sets
Christensen has defined a generalization of the property of being of Haar measure zero to subsets of (abelian) Polish groups which need not be locally compact; a recent paper of Hunt, Sauer, and Yorke defines the same property for Borel subsets of linear spaces, and gives a number of examples and applications. The latter authors use the term “shyness” for this property, and “prevalence” for the complementary property. In the present paper, we construct a number of examples of non-shy Borel sets...
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
Exhaustive measures in arbitrary topological vector 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.