Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Lectures on Gaussian Approximations with Malliavin Calculus Read chapter Read first chapter

2013 | OriginalPaper | Chapter

A Planar Borel Set Which Divides Every Non-negligible Borel Product

Author : Michel Émery

Published in: Séminaire de Probabilités XLV

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In the unit square [0, 1] ×[0, 1] endowed with the Lebesgue measure λ, we construct a Borel subset A with the following property: if U and V are any two non-negligible Borel subsets of [0, 1], then \(0 <\lambda {\bigl ( A \cap (U \times V )\bigr )} <\lambda (U \times V )\).

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Filtrations Indexed by Ordinals; Application to a Conjecture of S. Laurent
next chapter Characterising Ocone Local Martingales with Reflections
Footnotes
1
All linear notions (dimension, rank, independence) are understood with \(\mathbb{F}\) as the field of scalars.
 
2
A weaker hypothesis suffices, namely, for each i ∈ r there is at least one h ∈ H with \(h \cap r =\{ i\}\).
 
Literature
1.
C. Dellacherie, M. Émery, Filtrations indexed by ordinals; application to a conjecture of S. Laurent. Séminaire de Probabilités XLV, Springer Lecture Notes in Mathematics, vol. 2078 (Springer, Berlin, 2013), pp. 141–157
2.
J. Neveu, Mathematical Foundations of the Calculus of Probability (Holden-Day, San Francisco, 1965)
Metadata
Title
A Planar Borel Set Which Divides Every Non-negligible Borel Product
Author
Michel Émery
Copyright Year
2013
Publisher
Springer International Publishing
Book
Séminaire de Probabilités XLV

Print ISBN: 978-3-319-00320-7

Electronic ISBN: 978-3-319-00321-4

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-319-00321-4_5