set of measure zero sentence in Hindi
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- For instance, a Besicovitch showed that there are Besicovitch sets of measure zero.
- *" f " carries closed sets of measure zero onto closed sets of measure zero.
- *" f " carries closed sets of measure zero onto closed sets of measure zero.
- That means, in other words, that " T " preserves the concept of a set of measure zero.
- So the distributional derivatives are given by the usual derivatives off ? * " ? *, a set of measure zero.
- The equality should be understood as holding almost everywhere, that is, differing at most on a set of measure zero.
- A set is called a set of full measure if its complement, relative to X, is a set of measure zero.
- I'm aware there's some ambiguity for diadic rationals, but a set of measure zero won't matter for this question.
- We say that if some property holds at every point of a set of full measure ( or equivalently everywhere except on a set of measure zero ), it holds almost everywhere.
- Integration with respect to Lebesgue is independent of sets of measure zero, but integration with respect to the Dirac measure, which is what you are doing, cares about pointwise values.
- If u has a weak derivative, it is often written D ^ { \ alpha } u since weak derivatives are unique ( at least, up to a set of measure zero, see below ).
- It is sometimes said that the circle map maps the rationals, a set of measure zero at " K " = 0, to a set of non-zero measure for K \ neq 0.
- Then there is a ?-finite quasi-invariant measure ? on " X " which is unique up to measure equivalence ( that is any two such measures have the same sets of measure zero ).
- The integral makes sense because the set of directions where projection doesn't give a knot diagram is a set of measure zero and " n " ( " v " ) is locally constant when defined.
- Such functions are defined only up to a set of measure zero, and since the boundary \ partial \ Omega does have measure zero, any function in a Sobolev space can be completely redefined on the boundary without changing the function as an element in that space.
- The theorem is analogous to regular Fubini's theorem for the case where the considered function is a characteristic function of a set in a product space, with usual correspondences meagre set with set of measure zero, comeagre set with one of full measure, a set with Baire property with a measurable set.
- More specifically, a property holds almost everywhere if the set of elements for which the property does not hold is a set of measure zero ( Halmos 1974 ), or equivalently if the set of elements for which the property holds is complete, it is sufficient that the set is contained within a set of measure zero.
- More specifically, a property holds almost everywhere if the set of elements for which the property does not hold is a set of measure zero ( Halmos 1974 ), or equivalently if the set of elements for which the property holds is complete, it is sufficient that the set is contained within a set of measure zero.
- For every smooth test function \ phi \ in C _ c ^ \ infty ( \ Omega ) with compact support, then ( up to redefinition on a set of measure zero ) u \ in C ^ { \ infty } ( \ Omega ) is smooth and satisfies \ Delta u = 0 pointwise in \ Omega.
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