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'singular'
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| Title of object: |
singular |
| Canonical Name: |
SingularMeasures |
| Type: |
Definition |
| Created on: |
2003-02-09 10:36:10.192948-05 |
| Modified on: |
2003-02-09 10:44:15.522821-05 |
| Classification: |
msc:28A12 |
Revision comment (for changes between this and next version):
| Changes for correction #1628 ('singular measure not singular'). |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here |
Content:
Two measures $\mu$ and $\nu$ in a measurable space $(\Omega,\mathcal{A})$ are
called \emph{singular} if there exist two disjoint sets $A$ and $B$ in $\mathcal{A}$ such that $A\cup B =\Omega$ and $\mu(B)=\nu(A) = 0$.
This is denoted by $\mu\perp\nu$. |
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