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An integral in which there is a successive integration with respect to different variables, i.e. an integral of the form
7 KB (1,043 words) - 01:21, 7 May 2022
[[Category:Classical measure theory]]
A concept of classical measure theory.
3 KB (373 words) - 17:15, 18 August 2012
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The comparison of algorithms and the analysis of numerical problems in a Bayesian setting, cf. also [[Bayesi
6 KB (908 words) - 18:44, 21 March 2024
[[Category:Classical measure theory]]
...ebra]] $\mathcal{B}$ of subsets of a set $X$ and a [[Signed measure|signed measure]]
3 KB (403 words) - 10:49, 10 December 2012
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...valign="top">[a1]</TD> <TD valign="top"> M.M. Rao, "Measure theory and integration" , Wiley (Interscience) (1987) pp. Chapt. 7</TD></TR></table>
977 bytes (144 words) - 08:05, 6 June 2020
[[Category:Classical measure theory]]
...bra of sets|$\sigma$-algebra]] $\mathcal{B}$ of subsets of $X$, then $\mu$ and $\nu$ are said to be singular
3 KB (399 words) - 17:27, 18 August 2012
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be such a group and let $ \alpha $
3 KB (413 words) - 08:01, 6 June 2020
...all compact subsets, taking finite values on all compact subsets of $ G $, and satisfying either the condition of '''left-invariance''':
...rdingly, one speaks of a left- or right-invariant Haar measure. Every Haar measure is $ \mu $-'''regular''', i.e.,
6 KB (971 words) - 20:18, 23 April 2017
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...and most important case of a product of spaces, see the article [[Measure|Measure]]. A more general construction is given below. Let $ I $
4 KB (573 words) - 17:45, 4 June 2020
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...iple Riemann integral is based on the concept of a [[Jordan measure|Jordan measure]] $ \mu $.
11 KB (1,648 words) - 16:53, 20 January 2024
...Riemannian manifolds]] and which introduces a natural concept of [[Measure|measure]] on the manifold.
...basis) of $w_j$. Moreover, $|\omega (v_1, \ldots, v_n)|$ is the [[Lebesgue measure]] (i.e. the $n$-dimensional volume) of the [[Parallelopipedon|parallelopipe
7 KB (1,061 words) - 06:58, 29 June 2014
[[Category:Set functions and measures on topological spaces]]
The terminology ''Borel measure'' is used by different authors with different meanings:
5 KB (764 words) - 09:39, 16 August 2013
[[Category:Classical measure theory]]
A central theorem in classical measure theory, sometimes called
3 KB (451 words) - 17:37, 18 August 2012
''inner regular measure''
[[Category:Classical measure theory]]
4 KB (638 words) - 19:35, 1 January 2021
[[Category:Classical measure theory]]
===Definition and properties===
5 KB (691 words) - 09:52, 6 July 2013
[[Category:Classical measure theory]]
...em on the relation between the concepts of almost-everywhere convergence and uniform convergence of a sequence of functions. In literature it is somet
4 KB (595 words) - 17:27, 18 October 2012
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...B.J. Pettis needed to use this result but noted that no proof was supplied and then proceeded to give a proof ([[#References|[a6]]]; the proof is very sim
5 KB (714 words) - 15:30, 1 July 2020
[[Category:Classical measure theory]]
A concept in measure theory (see also [[Absolute continuity]]). If $\mu$ and $\nu$ are two measures on a [[Algebra of sets|σ-algebra]] $\mathcal{B}$ o
6 KB (957 words) - 07:56, 15 December 2016
[[Category:Classical measure theory]]
A classical theorem in measure theory first established by J. Radon and O.M. Nikodým, which has the following statement.
3 KB (484 words) - 12:09, 14 December 2012
[[Category:Classical measure theory]]
An outer measure is a [[Set function|set function]] $\mu$ such that
9 KB (1,397 words) - 10:08, 16 August 2013