[permalink] [id link]
* Every Borel set B ⊆ R < sup > n </ sup > is μ-measurable in the sense of Carathéodory's criterion: for every A ⊆ R < sup > n </ sup >,
from
Wikipedia
Some Related Sentences
Every and Borel
** Every infinite game in which is a Borel subset of Baire space is determined.
* Every Borel set E is outer regular:
Every random vector gives rise to a probability measure on R < sup > n </ sup > with the Borel algebra as the underlying sigma-algebra.
* Every open subset of X is a Borel set.
* Every projective set of reals -- and therefore every analytic set and every Borel set of reals -- is an element of L ( R ).
Every and set
: Every set has a choice function.
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.
** Well-ordering theorem: Every set can be well-ordered.
** 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.
** Antichain principle: Every partially ordered set has a maximal antichain.
* 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 non-empty set A contains an element B which is disjoint from A.
* 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 cofinal subset of a partially ordered set must contain all maximal elements of that set.
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 singleton set
Every processor or processor family has its own machine code instruction set.
Every set is a class, no matter which foundation is chosen.
Every non-empty totally ordered set is directed.
* 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 B
Every year, it invites entries of unpublished African-inspired stories written for an audience of 8 to 11-year-olds ( Category A ) or 12 to 15-year-olds ( Category B ) and by writers aged 18 or below ( the Rising Writer Prize ).
Every year since 1982, the W. C. Handy Music Festival is held in the Florence / Sheffield / Muscle Shoals area, featuring blues, jazz, country, gospel, rock music and R & B.
Every finite group of exponent n with m generators is a homomorphic image of B < sub > 0 </ sub >( m, n ).
The Pips recorded a second version of " Every Beat " with Bobby Robinson as the producer, and the song became a # 1 R & B and # 6 pop hit.
Every single that Bell produced for the Stylistics was a Top Ten R & B hit, and several —" You Are Everything ", " Betcha by Golly Wow!
" " Every Day " hit number two on the R & B charts, and sparked another LP — 1957 The Greatest!
Every other fret remains unaffected ( e. g. the 7th fret of an E-string will still play a B note for any capo position at or below the 7th fret ), and thus a performer does not need to adjust for or relearn the entire fretboard as they might with retuning.
B ' nai B ' rith also publishes program guides for local Jewish education programs and each year sponsors " Unto Every Person There is a Name ".
This means that A is not necessarily better than B, and B is not necessarily better than C. Every class is independent of the others.
Every degree of freedom in the energy is quadratic and, thus, should contribute k < sub > B </ sub > T to the total average energy, and k < sub > B </ sub > to the heat capacity.
* Every audience member had his or her own A / B / C / D keypad.
She appeared in Plaza Suite, Every Little Crook and Nanny, B. S.
* Stockham, Alice B Tokology: A Book for Every Woman, Sanitary Publishing Co., Illinois, 1886, with eight Color Plates in a sleeve inside the back cover.
Every other day, starting on the third day, the player can go after an A. P. B.
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.
B. Lippincott Company, but was reprinted once in 1959 by Pocket Books under the title Mr. Adam Was Wanted By Every Woman in the World.
Every weekend, the band would play the opening set for touring bands such as Earth, Wind and Fire, Stevie Wonder, James Brown and Kool & The Gang, and the charangueros became huge fans of both the music and stage shows of North American R & B.
Every injector they tested had detectable blood in a quantity sufficient to pass on a virus such as hepatitis B.
Every isogeny f: A → B is automatically a group homomorphism between the groups of k-valued points of A and B, for any field k over which f is defined.
2.251 seconds.