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Page "Banach space" ¶ 25

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Let and X

Let X be some repeatable process, and i be some point in time after the start of that process.

* Theorem Let X be a normed space.

* Corollary Let X be a reflexive normed space and Y a Banach space.

* Corollary Let X be a reflexive normed space.

Let V, W and X be three vector spaces over the same base field F. A bilinear map is a function

* Let X be a simply ordered set endowed with the order topology.

Let X denote a Cauchy distributed random variable.

Let X be a nonempty set, and let.

: Theorem on projections: Let the function f: X → B be such that a ~ b → f ( a )

Let X be a finite set with n elements.

" Let X be the unit Cartesian square ×, and let ~ be the equivalence relation on X defined by ∀ a, b ∈ (( a, 0 ) ~ ( a, 1 ) ∧ ( 0, b ) ~ ( 1, b )).

Let X i be the measured weight of the ith object, for i

Let X be a topological space, and let x 0 be a point of X.

Let be the conditional probability distribution function of Y given X.

Let ƒ be a function whose domain is the set X, and whose range is the set Y.

Let ( X i , f ij ) be an inverse system of objects and morphisms in a category C ( same definition as above ).

* Let the index set I of an inverse system ( X i , f ij ) have a greatest element m. Then the natural projection π m : X → X m is an isomorphism.

Let there be a finite sequence of positive integers X

Let X be a measurable space, let μ be a measure on X, and let N be a measurable set in X.

Let and Y

Let X and Y be objects of a category D. The product of X and Y is an object X × Y together with two morphisms

Let F: J → C be a diagram of type J in a category C. A cone to F is an object N of C together with a family ψ X : N → F ( X ) of morphisms indexed by the objects of J, such that for every morphism f: X → Y in J, we have F ( f ) o ψ X

Let F be a diagram that picks out three objects X, Y, and Z in C, where the only non-identity morphisms are f: X → Z and g: Y → Z.

Let ( X, Σ ) and ( Y, Τ ) be measurable spaces, meaning that X and Y are sets equipped with respective sigma algebras Σ and Τ.

Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step by step.

Let: X Y Z where we assume in the typical case that and.

* Let B be a base for X and let Y be a subspace of X.

Let Y = u ( X 1 , X 2 , ..., X n ) be a statistic whose pdf is g ( y ; θ ).

Let X be the set of numbers divisible by an element of Y.

Let X be a locally compact Hausdorff space equipped with a finite Radon measure μ, and let Y be a σ-compact Hausdorff space with a σ-finite Radon measure ρ.

Let φ: X → Y be a continuous and absolutely continuous function ( where the latter means that ρ ( φ ( E )) = 0 whenever μ ( E ) = 0 ).

Let X represent the space of signals that can be transmitted, and Y the space of signals received, during a block of time over the channel.

Let f: Y → X be a continuous map.

Let X be a Banach space and Y be a normed vector space.

Let X and Y be topological spaces.

Let X and Y be metric spaces with metrics d X and d Y .

Let and be

Let the open enemy to it be regarded as a Pandora with her box opened ; ;

Let every policeman and park guard keep his eye on John and Jane Doe, lest one piece of bread be placed undetected and one bird survive.

`` Let him be now ''!!

Let us assume that it would be possible for an enemy to create an aerosol of the causative agent of epidemic typhus ( Rickettsia prowazwki ) over City A and that a large number of cases of typhus fever resulted therefrom.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.

Let Af be the null space of Af.

Let N be a linear operator on the vector space V.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.

Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.

Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.

Let us take a set of circumstances in which I happen to be interested on the legislative side and in which I think every one of us might naturally make such a statement.

Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.

Let this be denoted by Af.

Let it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.

Let not your heart be troubled, neither let it be afraid ''.

The same God who called this world into being when He said: `` Let there be light ''!!

For those who put their trust in Him He still says every day again: `` Let there be light ''!!

Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.

Let her out, let her out -- that would be the solution, wouldn't it??

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