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exponential time, if T(n) is upper bounded by 2poly(n), where poly(n) is some polynomial in n. More formally, an algorithm is exponential time if T(n) is bounded...

they are continuous almost everywhere, relative to the Lebesgue measure. If t < 0 {\displaystyle t<0} then { x ∈ X : f ( x ) ≥ t } = X = { x ∈ X : f (...

following. If T is symmetric then T ⊂ T∗∗ ⊂ T∗. If T is closed and symmetric then T = T∗∗ ⊂ T∗. If T is self-adjoint then T = T∗∗ = T∗. If T is essentially...

first-order logic. The completeness theorem applies to any first-order theory: If T is such a theory, and φ is a sentence (in the same language) and every model...

in set theory (and in other sufficiently expressive axiomatic systems). If T is a theory and A is an additional axiom, T + A is said to be consistent...

other sentences. A sentence σ is independent of a given first-order theory T if T neither proves nor refutes σ; that is, it is impossible to prove σ from T...

different parts of the input function f ( τ ) {\displaystyle f(\tau )} ; If t {\displaystyle t} is a positive value, then g ( t − τ ) {\displaystyle g(t-\tau...

after Erich Leo Lehmann and Henry Scheffé, given their two early papers. If T is a complete sufficient statistic for θ and E(g(T)) = τ(θ) then g(T) is...

{\displaystyle f} acting on the distribution T . {\displaystyle T.} Proposition. If T {\displaystyle T} is a linear functional on C c ∞ ( U ) {\displaystyle C_{c}^{\infty...

with Tr ⁡ ( | T | ) < ∞ . {\displaystyle \operatorname {Tr} (|T|)<\infty .} If T is trace class then ‖ T ‖ 1 = sup { | Tr ⁡ ( C T ) | : ‖ C ‖ ≤ 1  and  C...

monotonic function, then f {\displaystyle f} is injective on its domain, and if T {\displaystyle T} is the range of f {\displaystyle f} , then there is an...

Not every theory is model-companionable, e.g. theory of groups. However if T is an ℵ 0 {\displaystyle \aleph _{0}} -categorical theory, then it always...

{\mathcal {T}}} , if T ⊢ ϕ {\displaystyle {\mathcal {T}}\vdash \phi } , then ϕ ∈ T {\displaystyle \phi \in {\mathcal {T}}} ; or, equivalently, if T ′ {\displaystyle...

said to be in the spectrum of a bounded linear operator T {\displaystyle T} if T − λ I {\displaystyle T-\lambda I} either has no set-theoretic inverse; or...

In linear algebra, linear transformations can be represented by matrices. If T {\displaystyle T} is a linear transformation mapping R n {\displaystyle \mathbb...

\left(A\left(x\otimes y\right)\right)=\left\langle Ax,y\right\rangle } . If T : H → H {\displaystyle T:H\to H} is a bounded compact operator with eigenvalues...

but not in X {\displaystyle X} ). Closed Graph Theorem for Banach spaces — If T : X → Y {\displaystyle T:X\to Y} is an everywhere-defined linear operator...

flows are worth 0 ( H ( u − t ) = 1  if  t < u , 0  if  t > u {\displaystyle H(u-t)=1{\text{ if }}t<u,0{\text{ if }}t>u} ), because they have already occurred...

is defined as rect ⁡ ( t a ) = Π ( t a ) = { 0 , if  | t | > a 2 1 2 , if  | t | = a 2 1 , if  | t | < a 2 . {\displaystyle \operatorname {rect} \left({\frac...

formally: if T ⊢ φ {\displaystyle {\mathcal {T}}\vdash \varphi } always implies φ ∈ T {\displaystyle \varphi \in {\mathcal {T}}} . If T {\displaystyle...