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case and interval
In this case, is the smallest σ-algebra that contains the open intervals of R. While there are many Borel measures μ, the choice of Borel measure which assigns for every interval is sometimes called " the " Borel measure on R. In practice, even " the " Borel measure is not the most useful measure defined on the σ-algebra of Borel sets ; indeed, the Lebesgue measure is an extension of " the " Borel measure which possesses the crucial property that it is a complete measure ( unlike the Borel measure ).
Caesar's 46 BCE ludi were hardly justified as munus after a 20 year interval since his father's death, in which case they were mere entertainment for political gain.
* The open interval ( a, b ) is homeomorphic to the real numbers R for any a < b. ( In this case, the bicontinuous forward mapping is given by and the inverse mapping is given by a scaled version of the function ).
Many car and engine manufacturers support extended drain intervals, but request extended drain interval certified oil used in that case ; and sometimes a special oil filter.
In the case where an individual end-to-end telecommunications service is provided by parallel channels, the parallel-channel signaling rate is given by, where PCSR is the total signaling rate for m channels, m is the number of parallel channels, T < sub > i </ sub > is the minimum interval between significant instants for the I-th channel, and n < sub > i </ sub > is the number of significant conditions of modulation for the I-th channel.
The interval between the 50 % points of the final amplitude is usually used to determine or define pulse duration, and this is understood to be the case unless otherwise specified.
After a few months or years ( the interval depending on the amount, or carefulness, of usage ), it should be checked again, as it may have been knocked, or gradually squeezed, out of position again, in which case it is once again adjusted back to zero.
In this model, patients may still be treated at the scene up to the skill level of the attending crew, and subsequently transported to definitive care, but in many cases the reduced skill set of the ambulance crew and the needs of the patient indicate a shorter interval for transport of the patient than is the case in the Franco-German model.
In this case, the measured beam intensities may be corrected by subtracting the intensity measured in the dark interval before the ratio is taken.
The theorem is named after Andrey Nikolayevich Tychonoff, who proved it first in 1930 for powers of the closed unit interval and in 1935 stated the full theorem along with the remark that its proof was the same as for the special case.
In general, point estimation should be contrasted with interval estimation: such interval estimates are typically either confidence intervals in the case of frequentist inference, or credible intervals in the case of Bayesian inference.
The interval between such treatments is typically in the range of one to four weeks, except in the case of self-treatment where daily practice is common.
In other cases, e. g. the case of a complete analytical theory of the motion of some astronomical body, all of the elements will usually be given in the form of polynomials in interval of time from the epoch, and they will also be accompanied by trigonometrical terms of periodical perturbations specified appropriately.
They are also totally disconnected ( connected components are points ), scattered ( every non-empty set has an isolated point ; in this case, just take the smallest element ), zero-dimensional ( the topology has a clopen basis: here, write an open interval ( β, γ ) as the union of the clopen intervals ( β, γ '+ 1 )=< nowiki ></ nowiki > for γ '< γ ).
This can pose a particular problem for programs that wake up at a fixed interval that aligns with the load-average sampling, in which case a process may be under-or over-represented in the load average numbers.
However, it is often the case that the function we are trying to integrate is not smooth over the interval.
The 95 % prediction interval, is often estimated by assuming a normal distribution of the measured parameter, in which case it can alternatively be defined as the interval limited by 1. 96 ( often rounded up to 2 ) population standard deviations from either side of the population mean ( also called the expected value ).
So unlike the previous case of x and 2x we don't get a proof of Legendre's conjecture even for all large n. Error estimates on the PNT are not ( indeed, cannot be ) sufficient to prove the existence of even one prime in this interval.
Since the unit interval is simply connected, the lifting property for paths is a special case of the lifting property for maps stated above.
The fact that the ostraca records the case of only one worker rather than an entire group of workmen means the necropolis scribe cannot be presumed – at first glance – to have committed a dating error in altering the unknown king's Year date in the interval between IV Peret 28 and I Shemu 13.
The original definition of the Riemann integral does not apply to a function such as on the interval ∞, because in this case the domain of integration is unbounded.

case and is
This is the only case in modern history of a people of Britannic origin submitting without continued struggle to what they view as foreign domination.
he is very close to being a mental case.
What was only a vague suspicion in the case of Sherlock Holmes now appears as a direct accusation: the private eye is in danger of turning into his opposite.
In the case of social decay, form is displaced simply by the process of dissolution with no form at the terminus of the process.
If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.
This text from Dr. Huxley is sometimes used by enthusiasts to indicate that they have the permission of the scientists to press the case for a wonderful unfoldment of psychic powers in human beings.
There may be a case of this sort, but it is not one we wish to argue, here.
In any case but the last, such a course is sure to avenge itself upon the individual ; ;
The first thing to do is get her some money by a temporary but definite adjustment pending a final disposition of the case.
Such, he implies, is the case with his friend, who is not really a new convert himself but merely a favorer of new converts.
Although because of the important achievements of nineteenth century scholars in the field of textual criticism the advance is not so striking as it was in the case of archaeology and place-names, the editorial principles laid down by Stevenson in his great edition of Asser and in his Crawford Charters were a distinct improvement upon those of his predecessors and remain unimproved upon today.
That fact is very clearly illustrated in the case of the many present-day intellectuals who were Communists or near-Communists in their youth and are now so extremely conservative ( or reactionary, as many would say ) that they can define no important political conviction that does not seem so far from even a centrist position as to make the distinction between Mr. Nixon and Mr. Khrushchev for them hardly worth noting.
In any case, who ever thought that New York is typical of anything??
American history should clinch the case when Congress is asked to approve.
Senator Mundt's gross distortion of President Eisenhower's conversation into a denunciation of President Kennedy as too left wing, a statement Mr. Eisenhower declared to be entirely false, is another case in point.
The Connally amendment says that the United States, rather than the court, shall determine whether a matter is essentially within the domestic jurisdiction of the United States in a case before the World Court to which the United States is a party.
If the case is thus determined by us to be domestic, the court has no jurisdiction.
Besides the lack of an adequate ethical dimension to the Governor's case, one can ask seriously whether our lead over the Russians in quality and quantity of nuclear weapons is so slight as to make the tests absolutely necessary.
In my own case, I submit that such reasonable and fair exercise is woefully lacking.
In connection with any claim decided by the Commission pursuant to this Title in which an award is made, the Commission may, upon the written request of the claimant or any attorney heretofore or hereafter employed by such claimant, determine and apportion the just and reasonable attorney's fees for services rendered with respect to such claim, but the total amount of the fees so determined in any case shall not exceed 10 per centum of the total amount paid pursuant to the award.
in the case of a partnership or corporation, the existence of which has been terminated and on behalf of which an award is made, payment shall be made, except as provided in paragraphs ( 3 ) and ( 4 ), to the person or persons found by the Comptroller General of the United States to be entitled thereto ; ;

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