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* Every set of reals in L ( R ) is Lebesgue measurable ( in fact, universally measurable ) and has the property of Baire and the perfect set property.
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Every and set
Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set.
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
* Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).
* Every continuous map from a compact space to a Hausdorff space is closed and proper ( i. e., the pre-image of a compact set is compact.
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 corporation, whether financial or union, as well as every division of the administration, were set up as branches of the party, the CEOs, Union leaders, and division directors being sworn-in as section presidents of the party.
Every DNS zone must be assigned a set of authoritative name servers that are installed in NS records in the parent zone, and should be installed ( to be authoritative records ) as self-referential NS records on the authoritative name servers.
Group actions / representations: Every group G can be considered as a category with a single object whose morphisms are the elements of G. A functor from G to Set is then nothing but a group action of G on a particular set, i. e. a G-set.
# " Personality " Argument: this argument is based on a quote from Hegel: " Every man has the right to turn his will upon a thing or make the thing an object of his will, that is to say, to set aside the mere thing and recreate it as his own ".
Every atom across this plane has an individual set of emission cones .</ p > < p > Drawing the billions of overlapping cones is impossible, so this is a simplified diagram showing the extents of all the emission cones combined.
* Every preorder can be given a topology, the Alexandrov topology ; and indeed, every preorder on a set is in one-to-one correspondence with an Alexandrov topology on that set.
Every binary relation R on a set S can be extended to a preorder on S by taking the transitive closure and reflexive closure, R < sup >+=</ sup >.
Every and reals
* Every real Banach algebra which is a division algebra is isomorphic to the reals, the complexes, or the quaternions.
* Every unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions.
* Every projective set of reals -- and therefore every analytic set and every Borel set of reals -- is an element of L ( R ).
Every and L
Every car uses either a 5. 0 L Ford " Boss 302 " SVO or a 5. 0 L Chevrolet small block race-engine ( depending on the make )-capable of producing between 460 and 485 kW ( 620 — 650 bhp ) of power, but generally quoted as a little over 450 kW ( 600 bhp ) in race trim.
Every square-integrable vector field u ∈ ( L < sup > 2 </ sup >( Ω ))< sup > 3 </ sup > has an orthogonal decomposition:
Every musician in L. A. wanted to participate, but soon Lennon's drinking and Spector's erratic behavior ( which included his firing a gun in the studio control room ) caused the sessions to break down.
* Let K < sup > a </ sup > be an algebraic closure of K containing L. Every embedding σ of L in K < sup > a </ sup > which restricts to the identity on K, satisfies σ ( L ) = L. In other words, σ is an automorphism of L over K.
Every non-trivial problem in L is complete under log-space reductions so weaker reductions are required to identify meaningful notions of L-completeness, the most common being first-order reductions.
Russell L. Ackoff wrote about complex problems as messes: " Every problem interacts with other problems and is therefore part of a set of interrelated problems, a system of problems ….
Professor Herman Bondi, who gave the first J. L. Synge Public Lecture in 1992, had this to say: " Every one of the other 88 % has been deeply influenced by his geometric vision and the clarity of his expression ".
Every L. A. # 1 song would be played in chronological order ( utilizing the older KHJ radio charts and other local charts ) from 1955 through 1985.
Every commutative von Neumann algebra on a separable Hilbert space is isomorphic to L < sup >∞</ sup >( X ) for some standard measure space ( X, μ ) and conversely, for every standard measure space X, L < sup >∞</ sup >( X ) is a von Neumann algebra.
Every Data Matrix is composed of two solid adjacent borders in an " L " shape ( called the " finder pattern ") and two other borders consisting of alternating dark and light " cells " or modules ( called the " timing pattern ").
Every year since 1994, Lloydies have climbed onto the top of Millikan Library to construct the Lloyd Christmas Tree, a monumental structure of numerous Christmas lights strung together to resemble a 10-story Christmas tree topped with a 12-feet-tall " L ." The latest off-campus pranks have been the pranking of MIT's Campus Preview Weekend, which included many Lloydies.
* James Allen ’ s Book of Meditations for Every Day in the Year ( 1913 ) of earlier texts, compiled by his wife Lily L. Allen