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

Wojciech Młotkowski; Noriyoshi Sakuma

Banach Center Publications (2011)

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

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topWojciech 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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