Note that a locally finite Borel measure automatically satisfies μ ( C ) < ∞ for every compact set C.

Note that the μ and ν summation indices range from 0 to 3: see Einstein notation.

Note that natural transformations can be composed: if μ ( X ): F ( X ) → G ( X ) is a natural transformation from the functor F: C → D to the functor G: C → D, and η ( X ): G ( X ) → H ( X ) is a natural transformation from the functor G to the functor H, then the collection η ( X ) μ ( X ): F ( X ) → H ( X ) defines a natural transformation from F to H. With this composition of natural transformations ( known as vertical composition, see natural transformation ), D < sup > C </ sup > satisfies the axioms of a category.

Note that τ, ( μ < sub > 1 </ sub >, Σ < sub > 1 </ sub >) and ( μ < sub > 2 </ sub >, Σ < sub > 2 </ sub >) may be all maximised independently of each other since they all appear in separate linear terms.

Note that the transition between " upper " (" contravariant ") and " lower " (" covariant ") vector or tensor components is trivial for a indices ( e. g. ), whereas for μ and ν it is nontrivial, corresponding e. g. to the usual Lorentz signature,.

Note that the probability mass function of a Poisson distribution for a count n with mean μ is given by

Note that if the measure spaces ( X, μ ) is a standard measure space ( that is X − N is a standard Borel space for some null set N and μ is a σ-finite measure ) then L < sup > 2 </ sup >< sub > μ </ sub >( X ) is separable.

( Note: So far as State Police cars are concerned, only their replacement is under this division ).

Note, however, that it is six inches shorter at the forward end.

Note another piece of wood six inches wide is fastened to the transom between these pieces.

Note: If 1/2-inch panel board is used inside and out, or 5/8-inch one side and 3/8-inch the other, and 1/8-inch glass is used, stock lumber in Af, Af, and Af can be used in making the glass panels.

Note that the mass threshold is four times that of 1958 Alpha and that the flux is one fifth as large.

Note that the mass scale is one to two orders of magnitude greater than some previously used ; ;

Note also that if Af, then Af is divisible by the polynomial p, because Af contains each Af as a factor.

Note that flexural strength is not always improved by simply increasing the density, nor is the change always proportional from one formulation to another.

Most European domestic power supplies run at 230 V, so the current drawn by a particular European appliance ( in Europe ) will be less than for an equivalent American one ( in the United States ).< ref group =" Note "> The formula for power is given by

Note that this premise uses the phrase " is not ", a form of " to be "; this and many other examples show that he did not intend to abandon " to be " as such.

Note: This list is limited to linguists who have worked specifically on the Altaic problem since the publication of the first volume of Ramstedt's Einführung in 1952.

Note that any model of ZF ¬ C is also a model of ZF, so for each of the following statements, there exists a model of ZF in which that statement is true.

Note that there is no directly corresponding concept in the German language.

Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

Note that the above formula is only applicable to classical ideal gases and not Bose – Einstein or Fermi gases.

Note that this pressure increase is more than a simple 10: 1 compression ratio would indicate ; this is because the gas is not only compressed, but the work done to compress the gas has also heated the gas and the hotter gas will have a greater pressure even if the volume had not changed.

Note that this is not the same as a monophyly in which all descendants of a common ancestor are included.

Note: because Solar System bodies are never perfect diffuse reflectors, astronomers use empirically derived relationships to predict apparent magnitudes when accuracy is required.

Note that this is subtly different to the ' thanks ' list in the original BBC Model B.

Note derivative is positive number | positive where green line appears, negative number | negative where red line appears, and zero ( number ) | zero where black line appears.

Note that is positive while is negative ; in any reversible work-extracting process, entropy is overall not increased, but rather is moved from a hot ( high-entropy ) system to a cold ( low-entropy one ), decreasing the entropy of the heat source and increasing that of the heat sink.

Note derivative is positive number | positive where green, negative number | negative where red, and zero ( number ) | zero where black

The other maxima occur at angles which are represented by non-zero integers m. Note that m can be positive or negative, resulting in diffracted orders on both sides of the zero order beam.

Note the difference between the positive and negative ranges.

Note that a positive phase shift, at a given moment of time, shifts the wave in the negative x-axis direction.

Note that this definition of the negative binomial distribution does not easily generalize to a positive, real parameter r.

( Note that (*) guarantees that either all three of U, V, W are positive, or else exactly two are negative.

Note that the magnetic flux is the net number of field lines passing through that surface ; that is, the number passing through in one direction minus the number passing through in the other direction ( see below for deciding in which direction the field lines carry a positive sign and in which they carry a negative sign ).

Note that the flux of E through a closed surface is not always zero ; this indicates the presence of " electric monopoles ", that is, free positive or negative charges.

Note that the above equation is flawed — as the temperature approaches zero, the entropy approaches negative infinity, in contradiction to the third law of thermodynamics.

Note that in order to act near optimally, the agent must reason about the long term consequences of its actions: In order to maximize my future income I better go to school now, although the immediate monetary reward associated with this might be negative.

Note the branch cut along the negative real axis, ending at − 1 / e.

Note that the reason we can discard the absolute value sign is that, as we observed earlier, ( x − 4 )< sup > 2 </ sup > + 9 can never be negative.

Note that a negative number with greater magnitude is considered less.

( Note however that the formula is not valid when is a negative integer or zero.

Note that negative polarity can be triggered not only by direct negatives such as " not " or " never ", but by words such as " doubt " or " hardly " (" I doubt he has ever owed anything to anyone " or " He has hardly ever owed anything to anyone ").

Note that the ( negative ) gradient at a point is orthogonal to the contour line going through that point.

" The World Council of Churches in The Challenge of Proselytism and the Calling to Common Witness states the following: ( Note: this document uses proselytism in the negative sense only.

Note that there is no value judgment attached to the terms negative or positive.

Note that there is also a small component of force in the negative y direction ( F < sub > y </ sub >).

Note that ( as shown above ) the signs of reactances become reversed in the admittance domain, i. e. capacitive susceptance is positive and inductive suceptance is negative.

Note also that while an anti de Sitter space would describe general relativity with a negative cosmological constant in five dimensions ( four for spacetime and one for the effect of the cosmological constant ), the idea is actually more general.