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Start Over Subject monotone measure

1. Concentrated monotone measures with non-unique tangential behavior in $\mathbb{R}^3$

Creator:
Černý, Robert, Kolář, Jan, and Rokyta, Mirko
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
monotone measure, monotonicity formula, and tangent measure
Language:
English
Description:
We show that for every $\varepsilon >0$ there is a set $A\subset \mathbb{R}^3$ such that ${\Cal H}^1\llcorner A$ is a monotone measure, the corresponding tangent measures at the origin are non-conical and non-unique and ${\Cal H}^1\llcorner A$ has the $1$-dimensional density between $1$ and $2+\varepsilon $ everywhere in the support.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. The Choquet integral as Lebesgue integral and related inequalities

Creator:
Mesiar, Radko, Li, Jun, and Pap, Endre
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Choquet integral, comonotone functions, integral inequalities, monotone measure, and modularity
Language:
English
Description:
The integral inequalities known for the Lebesgue integral are discussed in the framework of the Choquet integral. While the Jensen inequality was known to be valid for the Choquet integral without any additional constraints, this is not more true for the Cauchy, Minkowski, Hölder and other inequalities. For a fixed monotone measure, constraints on the involved functions sufficient to guarantee the validity of the discussed inequalities are given. Moreover, the comonotonicity of the considered functions is shown to be a sufficient constraint ensuring the validity of all discussed inequalities for the Choquet integral, independently of the underlying monotone measure.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public