# Symmetrization of probability measures, pushforward of order 2 and the Boolean convolution

• Volume: 96, Issue: 1, page 271-276
• ISSN: 0137-6934

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## Abstract

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We study relations between the Boolean convolution and the symmetrization and the pushforward of order 2. In particular we prove that if μ₁,μ₂ are probability measures on [0,∞) then ${\left(\mu ₁⨄\mu ₂\right)}^{s}=\mu {₁}^{s}⨄\mu {₂}^{s}$ and if ν₁,ν₂ are symmetric then ${\left(\nu ₁⨄\nu ₂\right)}^{\left(2\right)}=\nu {₁}^{\left(2\right)}⨄\nu {₂}^{\left(2\right)}$. Finally we investigate necessary and sufficient conditions under which the latter equality holds.

## How to cite

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Wojciech Młotkowski, and Noriyoshi Sakuma. "Symmetrization of probability measures, pushforward of order 2 and the Boolean convolution." Banach Center Publications 96.1 (2011): 271-276. <http://eudml.org/doc/281922>.

@article{WojciechMłotkowski2011,
abstract = {We study relations between the Boolean convolution and the symmetrization and the pushforward of order 2. In particular we prove that if μ₁,μ₂ are probability measures on [0,∞) then $(μ₁ ⨄ μ₂)^\{s\} = μ₁^\{s\} ⨄ μ₂^\{s\}$ and if ν₁,ν₂ are symmetric then $(ν₁ ⨄ ν₂)^\{(2)\} = ν₁^\{(2)\} ⨄ ν₂^\{(2)\}$. Finally we investigate necessary and sufficient conditions under which the latter equality holds.},
author = {Wojciech Młotkowski, Noriyoshi Sakuma},
journal = {Banach Center Publications},
keywords = {symmetrization; pushforward of order 2; Boolean convolution},
language = {eng},
number = {1},
pages = {271-276},
title = {Symmetrization of probability measures, pushforward of order 2 and the Boolean convolution},
url = {http://eudml.org/doc/281922},
volume = {96},
year = {2011},
}

TY - JOUR
AU - Wojciech Młotkowski
AU - Noriyoshi Sakuma
TI - Symmetrization of probability measures, pushforward of order 2 and the Boolean convolution
JO - Banach Center Publications
PY - 2011
VL - 96
IS - 1
SP - 271
EP - 276
AB - We study relations between the Boolean convolution and the symmetrization and the pushforward of order 2. In particular we prove that if μ₁,μ₂ are probability measures on [0,∞) then $(μ₁ ⨄ μ₂)^{s} = μ₁^{s} ⨄ μ₂^{s}$ and if ν₁,ν₂ are symmetric then $(ν₁ ⨄ ν₂)^{(2)} = ν₁^{(2)} ⨄ ν₂^{(2)}$. Finally we investigate necessary and sufficient conditions under which the latter equality holds.
LA - eng
KW - symmetrization; pushforward of order 2; Boolean convolution
UR - http://eudml.org/doc/281922
ER -

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