Examples of 'lebesgue measure' in a sentence
Meaning of "lebesgue measure"
Lebesgue measure is a concept in mathematical analysis that assigns a measure to subsets of Euclidean spaces, generalizing the notion of length, area, and volume. It allows for a more flexible and powerful way of measuring sets, particularly those with irregular shapes
Show more definitions
- A unique complete translation-invariant measure for the σ-algebra which contains all k-cells in a given Euclidean space, and which assigns a measure to each k-cell which is equal to that k-cell's volume (as defined in Euclidean geometry: i.e., the volume of the k-cell equals the product of the lengths of its sides).
How to use "lebesgue measure" in a sentence
Basic
Advanced
lebesgue measure
We prove the existence of invariant probability measures absolutely continuous with respect to lebesgue measure.
Lebesgue measure on Euclidean space is locally finite.
A particularly important example is the Lebesgue measure.
Consider the Lebesgue measure on the real line.
That is except possibly on a set of Lebesgue measure zero.
Consider the Lebesgue measure on the half line.
It follows that g has a set of discontinuities of positive Lebesgue measure.
An approximation of the Lebesgue measure of the spectrum is obtained.
This is for example the case for the Lebesgue measure.
Lambda denotes the Lebesgue measure in mathematical set theory.
Such distributions are not absolutely continuous with respect to Lebesgue measure.
The Lebesgue measure on the line and in Rn.
A simple example of a doubling measure is Lebesgue measure on a Euclidean space.
The Lebesgue measure also has the property of being σ-finite.
This applies in particular when and when is the Lebesgue measure.
See also
A Euclidean space with Lebesgue measure is a measure space.
This measure is absolutely continuous with respect to the Lebesgue measure.
Inclusion of Lebesgue measure and Lebesgue integrals.
The Cantor set is an example of an uncountable set that has Lebesgue measure zero.
The circle group T with the Lebesgue measure is an immediate example.
One may have a similar objective when considering Hausdorff measure instead of Lebesgue measure.
This is called Lebesgue measure.
So that, in particular, μ is absolutely continuous with respect to Lebesgue measure.
With respect to Lebesgue measure.
It can be shown that there is no infinite-dimensional analogue of Lebesgue measure.
Has positive Lebesgue measure.
That 's because there is no infinite dimensional analog to Lebesgue measure.
Is standard Lebesgue measure.
The area of a Sierpinski triangle is zero in Lebesgue measure.
Where, is the Lebesgue measure of a measurable set.
A similar argument implies that the limit set has Lebesgue measure zero.
Chapter 2 deals with Lebesgue measure and integration.
Let M be a set of real numbers with positive Lebesgue measure.
Lebesgue measure is both locally finite and inner regular, and so it is a Radon measure.
Where is the standard Lebesgue measure.
See Lebesgue measure and Banach-Tarski paradox.
The construction of Lebesgue measure.
The Lebesgue measure also has the property of being Ï-finite.
More precisely, its Lebesgue measure is zero.
The real line carries a canonical measure, namely the Lebesgue measure.
The restriction of the Lebesgue measure to any convex set is also log-concave.
Working on his own, he rediscovered the Lebesgue measure.
Preserving Lebesgue measure, for which Lebesgue measure is not ergodic.
Nowhere dense but has a Lebesgue measure of ½.
Lebesgue measure on Rn ( with its Borel topology and σ-algebra ) is strictly positive.
Every strong measure zero set has Lebesgue measure 0.
For example, Lebesgue measure on the real numbers is not finite, but it is σ-finite.
Any countable set of real numbers has Lebesgue measure 0.
On the real line consider the Lebesgue measure and its corresponding σ-algebra Σ.
In the continuous univariate case above, the reference measure is the Lebesgue measure.
You'll also be interested in:
Examples of using Lebesgue
Show more
Lebesgue theorem for functions of bounded variation
Where the integral is to be understood in the usual lebesgue sense
Lebesgue integral in the abstract space
Examples of using Measure
Show more
It was an emergency measure but overcrowding is still a problem
Measure the difference between the markings
The unit of measure for water pressure
