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It is shown that if A ⊂ ℝ has the same constant shade with respect to all Banach measures, then the same is true of any similarity transformation of A and the shade is not changed by the transformation. On the other hand, if A ⊂ ℝ has constant μ-shade with respect to some fixed Banach measure μ, then the same need not be true of a similarity transformation of A with respect to μ. But even if it is, the μ-shade might be changed by the transformation. To prove such a μ exists, a Hamel basis with some...

Strict topology and perfect measures

Surjit Singh Khurana, Jorge E. Vielma (1990)

Czechoslovak Mathematical Journal

Strong continuity of invariant probability charges

Harald Luschgy, Sławomir Solecki (2004)

Colloquium Mathematicae

Consider a semigroup action on a set. We derive conditions, in terms of the induced action of the semigroup on {0,1}-valued probability charges, which ensure that all invariant probability charges are strongly continuous.

Subsets of the plane with small linear sections and invariant extensions of the two-dimensional Lebesgue measure.

Kharazishvili, A. (1999)

Georgian Mathematical Journal

Symmetric and Zygmund measures in several variables

Evgueni Doubtsov, Artur Nicolau (2002)

Annales de l’institut Fourier

Let $ω : (0, \infty) \to (0, \infty)$ be a gauge function satisfying certain mid regularity conditions. A (signed) finite Borel measure $μ \in ℝ^{n}$ is called $ω$ -Zygmund if there exists a positive constant $C$ such that $| μ (Q_{+}) - μ (Q_{-}) | \leq C ω (ℓ (Q_{+})) | Q_{+} |$ for any pair $Q_{+}, Q_{-} \subset ℝ^{n}$ of adjacent cubes of the same size. Similarly, $μ$ is called an $ω$ - symmetric measure if there exists a positive constant $C$ such that $| μ (Q_{+}) / μ (Q_{-}) - 1 | \leq C ω (ℓ (Q_{+}))$ for any pair $Q_{+}, Q_{-} \subset ℝ^{n}$ of adjacent cubes of the same size, $ℓ (Q_{+}) = ℓ (Q_{-}) < 1$ . We characterize Zygmund and symmetric measures in terms of their harmonic extensions. Also, we show that the quadratic condition...

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Displaying 181 – 200 of 236

Some properties of the density topology with respect to an extension of the Lebesgue measure.

Some remarks concerning finitely subadditive outer measures with applications.

Some remarks on the space $R^{2} (E)$ .

Some Vitali theorems for Lebesgue Measure.

Sous-mesures symétriques sur un ensemble fini

Special measures and repleteness.

Stretched shadings and a Banach measure that is not scale-invariant

Strict topology and perfect measures

Strong continuity of invariant probability charges

Subsets of the plane with small linear sections and invariant extensions of the two-dimensional Lebesgue measure.

Symmetric and Zygmund measures in several variables

The absolute continuity of functions defined on the $σ$ -ring generated by a ring

The atoms of a countable sum of set functions

The Hahn-Banach theorem implies the Banach-Tarski paradox

The Hausdorff a-Dimensional Measures of the Level Sets and the Graph of the TV-Parameter Wiener Process.

The Kantorovič-Rubinstein distance

The Kantorovič-Rubinstein distance

The Lebesgue integral a little over 100 years later.

The Necessity of Strongly Subadditive Capacities for Neyman-Pearson Minimax Tests.

The pathological infinity of measures

Currently displaying 181 – 200 of 236