Note that the above only becomes an issue if the user wishes to ( or has to ) continue to send e-mail remotely, using the same SMTP server which they were previously accessing locally.

Note that neither of these statements implies the other, since there are complete metric spaces which are not locally compact ( the irrational numbers with the metric defined below ; also, any Banach space of infinite dimension ), and there are locally compact Hausdorff space which are not metrizable ( for instance, any uncountable product of non-trivial compact Hausdorff spaces is such ; also, several function spaces used in Functional Analysis ; the uncountable Fort space ).

Note: there were more than 11 million vehicles in Iran by 2010 mostly manufactured or assembled locally.

Note that locally an embedded surface always has two sides, so a near-sighted ant crawling on a one-sided surface would think there is an " other side ".

Note that for positive semidefinite and negative semidefinite Hessians the test is inconclusive ( yet a conclusion can be made that f is locally convex or concave respectively ).

Note that the neighborhood U need not be simply connected: though every loop in U must be contractible within X, the contraction is not required to take place inside of U. For this reason, a space can be semi-locally simply connected without being locally simply connected.

Note that A. Connes also proved that the von Neumann group algebra of any connected locally compact group is hyperfinite, so the last condition no longer applies in the case of locally compact groups.

Note: “ Three-octet values occupying the same fields as OUIs can occupy, but with the next-to-LSB of the first octet set to 1, are locally assigned and have no relationship to the IEEE-assigned values ...”.

Note that the remote application runs just as it would locally.

Note also that although local diffeomorphisms preserve differentiable structure locally, one must be able to " patch up " these ( local ) diffeomorphisms to ensure that the domain is the entire ( smooth ) manifold.

( Note that the empty set is considered finite, with cardinality zero.

Note: For any arbitrary number of propositional constants, we can form a finite number of cases which list their possible truth-values.

Note that < em > finite </ em > in this definition is essential.

Note that every part of the machine — its state and symbol-collections — and its actions — printing, erasing and tape motion — is finite, discrete and distinguishable ; it is the potentially unlimited amount of tape that gives it an unbounded amount of storage space.

A set T of real numbers ( red and green balls ), a subset S of T ( green balls ), and the infimum of S. Note that for finite set s the infimum and the minimum are equal.

Note that, as an asymptotic expansion, this series is not convergent: it is a reasonable approximation only if the series is truncated at a finite number of terms, and only large values of x are employed.

Note that this concept of boundedness has nothing to do with finite size, and that a subset S of a bounded poset P with as order the restriction of the order on P is not necessarily a bounded poset.

Note that the Bernstein-von Mises theorem asserts here the asymptotic convergence to the " true " distribution because the probability space corresponding to the discrete set of events is finite ( see above section on asymptotic behaviour of the posterior ).

Note that although s and S are infinite, this works for finite matrices by only considering Stirling numbers up to some number N.

Note that the sequence of groups and homomorphisms may be either finite or infinite.

Note that the vertex degrees must be finite, but need not be bounded: it is possible to have one vertex of degree 10, another of degree 100, a third of degree 1000, and so on.

( Note, however, that even if we have gotten to the correct answer ( the end of the finite sequence ) we are never sure that we have the correct answer.

Note, that the right hand side only contains Ramsey numbers for c − 1 colours and 2 colours, and therefore exists and is a finite number t, by the inductive hypothesis.

Note that one may need to require ' to be absolutely integrable with respect to the weight ' in order for this integral to be finite.

Note that, commonly, 2 < sup > ω </ sup > is referred to simply as the Cantor set, while the term Cantor space is reserved for the more general construction of D < sup > S </ sup > for a finite set D and a set S which might be finite, countable or possibly uncountable.

Note that there are other notions of compactness in mathematics ; also, the term " finite " in its normal set theoretic meaning does not coincide with the order-theoretic notion of a " finite element ".

Note also that this definition is slightly more general than the one given by since it requires only to consider finite partitions of the space ': this implies that it can be used also to define the total variation on finite-additive measures.

Note that the formulae here reduce to the case of a finite or infinite mixture if the density w is allowed to be a generalised function representing the " derivative " of the cumulative distribution function of a discrete distribution.

Note: the images linked to in the following table do NOT take into account the finite speed of light.

Note: the image linked to in the following table does not take into account the finite speed of light.

Note that this is true regardless of which is used, however the midpoint approximation tends to be more accurate for finite.

Note that, as with any finite configuration in the real projective plane, this construction can be perturbed so that all points are finite, without changing the number of ordinary lines.

Note that the boldface hierarchy is just the standard hierarchy of Borel sets.

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 that the set of ∞- Borel sets may not actually be closed under wellordered union ; see below.

Note that as an income-based measure of poverty, this omits the effect of some other factors that may affect economic wellbeing, such as the availability of free health care and education.

Note that in a few cases the accidental might change the note by more than a semitone: for example, if a G sharp is followed in the same measure by a G flat, the flat sign on the latter note means it will be two semitones lower than if no accidental were present.

Note: Heuristic routing allows a measure of route optimization based on recent empirical knowledge of the state of the network.

Note, each barred section represents one measure, for a total of 16 measures.

Note, each barred section represents one measure, for a total of 16 measures.

Note that the fact that there is no way to trisect an angle in general with just a compass and a straightedge does not mean that it is impossible to trisect all angles: for example, it is relatively straightforward to trisect a right angle ( that is, to construct an angle of measure 30 degrees ).

Note that both of these are probabilities in a measure theoretic sense, and neither of these is the true probability of expiring in-the-money under the real probability measure.

Note that although mileposts measure the distance to Preston Brook and Shardlow, Derwent mouth is a mile or so beyond Shardlow.

Note that the quoted precipitation is a measure of its equivalence to water, rather than being the actual depth of snow.

Note that the denominator is simply the measure of the set X ( However, this formula cannot be applied if the set X has zero measure, or if either integral diverges.

Note that you have to measure the amounts in the same unit that was used to calculate the intensive property from the extensive property.

Note that this measure is only effective if the interval between cars is reduced, not the distance itself.

He acquiesced in the purchase of the Suez Canal shares, a measure then considered dangerous by many people, but ultimately most successful ; he accepted the Andrassy Note, but declined to accede to the Berlin Memorandum.

Note that centimeters are often used to measure length in the semiconductor industry, which is why they are used here instead of the SI units of meters.

Note that the term double bar refers not to a type of bar ( i. e., measure ), but to a type of bar-line.

Note that ROUGE is similar to the BLEU measure for machine translation, but BLEU is precision-based, because translation systems favor accuracy.

( Note that some of the properties of the Lebesgue integral fail here, since our measure is only finitely additive.

Note that above, the risk neutral formula does not refer to the volatility of the underlying – p as solved, relates to the risk-neutral measure as opposed to the actual probability distribution of prices.

Note that the symmetric difference of two distinct sets can have measure zero ; hence the pseudometric as defined above need not to be a true metric.

Note that rail neutral temperature does not actually measure the temperature of the rail.

Note that the preceding measure words are singular in form.

Note that this energy function belongs to a general class of models in physics, under the name of Ising models ; these in turn are a special case of Markov networks, since the associated probability measure, the Gibbs measure, has the Markov property.