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Difference between revisions of "Almost-everywhere"

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''for almost all <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a011/a011940/a0119401.png" /> (with respect to a measure <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a011/a011940/a0119402.png" />)''
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''for almost all $x$ (with respect to a measure $\mu$)''
  
An expression indicating that one speaks about all <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a011/a011940/a0119403.png" /> of a measure space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a011/a011940/a0119404.png" /> with the possible exception of some set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a011/a011940/a0119405.png" /> of measure zero: <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a011/a011940/a0119406.png" />.
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An expression indicating that one speaks about all $x$ of a measure space $X$ with the possible exception of some set $A\subseteq X$ of measure zero: $\mu(A)=0$.

Latest revision as of 17:37, 11 April 2014

for almost all $x$ (with respect to a measure $\mu$)

An expression indicating that one speaks about all $x$ of a measure space $X$ with the possible exception of some set $A\subseteq X$ of measure zero: $\mu(A)=0$.

How to Cite This Entry:
Almost-everywhere. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Almost-everywhere&oldid=12277
This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article