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Every random vector gives rise to a probability measure on R < sup > n </ sup > with the Borel algebra as the underlying sigma-algebra.
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Every and random
Every physical system, however, when microscopically examined, shows apparently random microscopic statistical fluctuations in its thermodynamic variables of state ( entropy, temperature, pressure, etc .).
Every two months these bags were taken from the church of Santa Croce, where they were ordinarily kept, and in a short ceremony drawn out at random.
Every club in the league competes in this knockout tournament with 2 teams being given a random bye to the 2nd Round.
Every year the Lions host the Harvey Martin Classic at the Cotton Bowl in Dallas and play host to a random LSC opponent to reach out to the numerous Dallas alumni and also most of the Lion football players are from the DFW area.
Every 3 helis destroyed would give players a weapon or an extra ( see below ) or if the player had destroyed the heli from above ( using a hyperjump ) a random weapon smaller in quantity was gained.
Every and vector
Every subset A of the vector space is contained within a smallest convex set ( called the convex hull of A ), namely the intersection of all convex sets containing A.
Every vector v in determines a linear map from R to taking 1 to v, which can be thought of as a Lie algebra homomorphism.
Every vector space has a basis, and all bases of a vector space have the same number of elements, called the dimension of the vector space.
Every normed vector space V sits as a dense subspace inside a Banach space ; this Banach space is essentially uniquely defined by V and is called the completion of V.
Every finite-dimensional vector space is isomorphic to its dual space, but this isomorphism relies on an arbitrary choice of isomorphism ( for example, via choosing a basis and then taking the isomorphism sending this basis to the corresponding dual basis ).
Every continuous function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.
Every finite-dimensional Hausdorff topological vector space is reflexive, because J is bijective by linear algebra, and because there is a unique Hausdorff vector space topology on a finite dimensional vector space.
Every coalgebra, by ( vector space ) duality, gives rise to an algebra, but not in general the other way.
* Every holomorphic vector bundle on a projective variety is induced by a unique algebraic vector bundle.
For example, second-order arithmetic can express the principle " Every countable vector space has a basis " but it cannot express the principle " Every vector space has a basis ".
Many principles that imply the axiom of choice in their general form ( such as " Every vector space has a basis ") become provable in weak subsystems of second-order arithmetic when they are restricted.
Every vector space is free, and the free vector space on a set is a special case of a free module on a set.
Every and gives
Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra.
Every LORAN chain in the world uses a unique Group Repetition Interval, the number of which, when multiplied by ten, gives how many microseconds pass between pulses from a given station in the chain.
Every year, the International Documentary Festival in Amsterdam ( IDFA ) gives an acclaimed filmmaker the chance to screen his or her personal Top 10 favorite films.
* Every finite topological space gives rise to a preorder on its points, in which x ≤ y if and only if x belongs to every neighborhood of y, and every finite preorder can be formed as the specialization preorder of a topological space in this way.
Every thing depends upon the evil of the second order ; it is this which gives to such actions the character of crime, and which makes punishment necessary.
Every adjunction 〈 F, G, ε, η 〉 gives rise to an associated monad 〈 T, η, μ 〉 in the category D. The functor
Every ticket is provided with a bar code that gives information about the time the visitor stepped into the museum.
Every broadcasting company has members and the number of members gives them a status that is connected to the number of hours of broadcasting.
The WBC launched a website called Priests Rape Boys in which they criticize the Roman Catholic Church because of the Catholic sex abuse scandal, saying, " Every time any person gives any amount of money to the Catholic Church, that person is paying the salary of pedophile rapists.
Every year, the magazine gives out its Utne Independent Press Awards, which honor alternative and independent magazines from around the world.
This flat may be identified with the partition of the vertices of into the connected components of the subgraph formed by: Every set of edges having the same closure as gives rise to the same partition of the vertices, and may be recovered from the partition of the vertices, as it consists of the edges whose endpoints both belong to the same set in the partition.
Every sequence of A, B, and C without immediate repetition of the same one is possible and gives an equally dense packing for spheres of a given radius.
Every year the American Society of Architectural Illustrators gives out the Hugh Ferriss Memorial Prize for architectural rendering excellence.
Every year, the IDFA, International Documentary Festival in Amsterdam, gives an acclaimed filmmaker the chance to screen his or her personal Top 10 favorite films.
Every year, she gives a speech to cadets from throughout Civil Air Patrol at the National Honor Guard Academy and also to a gathered assembly of basic cadets and staff at the Civil Air Patrol's Tri-Wing Encampment, held by Maryland Wing.
Every episode gives credits to James Burrows, Glen Charles and Les Charles, the creators of Cheers, the show where the character of Dr. Frasier Crane originated.