In practice, the use of Baire measures on Baire sets can often be replaced by the use of regular Borel measures on Borel sets.
12.
Note that since the Haar measure is a Borel measure, in particular gives finite mass to compact subsets, the second definition is more inclusive.
13.
The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure.
14.
Lebesgue measure is an example of a complete measure; in some constructions, it's defined as the completion of a non-complete Borel measure.
15.
It is known, for instance, that every continuous translation invariant continuous linear operator on " L " 1 is the convolution with a finite Borel measure.
16.
Thus, this theorem is also true for every finite Borel measure on "'R " "'n " instead of Lebesgue measure, see Discussion.
17.
A Borel measure ? on X is boundedly finite if ? ( A ) M _ X be the space of all boundedly finite measures on \ mathfrak { B } ( X ).
18.
Consequently, the completion procedure is needed to extend the Borel measure into the Lebesgue measure, or to extend the product of two Lebesgue measures to give the Lebesgue measure on the product space.
19.
A current such that "'M "'( " T " ) < " is representable by integration of a regular Borel measure by a version of the Riesz representation theorem.
20.
Other'named'measures used in various theories include : Borel measure, Jordan measure, ergodic measure, Euler measure, Gaussian measure, Baire measure, Radon measure, Young measure, and strong measure zero.
How to say borel measure in Hindi and what is the meaning of borel measure in Hindi? borel measure Hindi meaning, translation, pronunciation, synonyms and example sentences are provided by Hindlish.com.
