Given also a measure on set, then, sometimes also denoted or, has as its vectors equivalence classes of measurable functions whose absolute value's-th power has finite integral, that is, functions for which one has

Given our political differences, people are sometimes surprised how close Ronnie and I have been to the Kennedy family.

Given a context pertaining to a specific OSI layer, PDU is sometimes used as a synonym for its representation at that layer.

Given these costs, governments are sometimes hesitant to participate, because benefits are often assumed not to outweigh the costs.

Given the potential for sampling biases of individual survey reports, researchers and investors try sometimes to average the values of different index reports into a single aggregated measure of consumer confidence.

Given the dangerous and clandestine criminal nature of people smuggling operations, smuggled persons are sometimes at risk of becoming victims of other crimes.

Given the decreasing influence of the movement, its name is sometimes applied in a broader sense to any modern practice related to folklore.

Given its proximity to Manhattan, it is sometimes referred to as New York City's sixth borough.

Given a rebbe's physical awareness of God, and the Rebbe's transcendent perception of Godliness, many hasidim take special care to observe the specific and sometimes minute practices of their Rebbe.

Given the prevalence of-assa place-names and words scattered around all sides of the Aegean Sea, this possessive suffix was sometimes considered evidence of a shared non-Indo-European language or an Aegean Sprachbund preceding the arrivals of Luwians and Greeks.

Given the proximity of Gateshead to Newcastle, just south of the River Tyne from the city centre, it is sometimes referred to as being a part of Newcastle.

Given its relative proximity with the cold to frigid air masses in Siberia, extreme lows are recorded in wintertime, sometimes well below.

Given a manifold with a submanifold, one sometimes says can be knotted in if there exists an embedding of in which is not isotopic to.

Given the frenetic pace at which he worked, Offenbach sometimes used the same material in more than one opera.

Given the proportions of his body, and the fact that in adulthood he was sometimes mistaken for a small child, it is likely that Joseph was a pituitary dwarf, not a dwarf of the achondroplasic variety.

Given their common legal context, the two are sometimes confused with one another, although they are unrelated.

Given an operator, it is sometimes useful to break up the spectrum into various parts.

Given these considerations, many experts believe that CLOS missiles are not as ideally suited for untrained personnel use as are IR missiles, which sometimes are referred to as “ fire and forget ” missiles.

Given the tonal design of the train whistle, the sound level, how often trains pass through a given community, the number of grade crossings in proximity, and the time of day ( night ) of occurrence, community residents residing near crossing sometimes feel that train whistles have a serious detrimental effect on the quality of life despite the gain in safety that sounding the horn provides to motorists.

Given years of practice, symbol shorthand writers could sometimes acquire skills of 150 or even 200 words per minute, which might have qualified them for demanding positions such as court reporting, typically dominated today by machine shorthands.

Given the social nature of the interview, applicant responses to interview questions and interviewer evaluations of those responses are sometimes influenced by constructs beyond those the questions were intended to assess, making it extremely difficult to tease out the specific constructs measured during the interview.

Given that omniverse is the largest set conceptualized by humanity, such a view is sometimes called " the end of infinity ".

Given a finite family of rings R < sub > 1 </ sub >, ..., R < sub > n </ sub >, the direct product of the R < sub > i </ sub > is sometimes called the direct sum.

Given investigators desire to choose larger margins to decrease the sample size needed to perform a trial, the chosen margin is sometimes larger than the effect size of the control compared to placebo.

Given a small ball or marbles, he would invent games and play by himself for hours.

Given the small population of the region ( compared with the Central Canadian provinces or the New England states ), the regional economy is a net exporter of natural resources, manufactured goods, and services.

Given the difficulty of finding exact solutions, Einstein's field equations are also solved frequently by numerical integration on a computer, or by considering small perturbations of exact solutions.

Given the overall size of trade between Mexico and the United States, there are remarkably few trade disputes, involving relatively small dollar amounts.

Given its small domestic market but favourable location and a superb transport and communications base, Namibia is a leading advocate of regional economic integration.

Given typical workloads, Cray felt that the small cost incurred by being required to break large sequential memory accesses into segments was a cost well worth paying.

Given the small temperature range kinetic studies occur in, it is reasonable to approximate the activation energy as being independent of the temperature.

Given the type of warfare that had been carried out in the conflict — wherein highly mobile groups of soldiers and rebels continued to move to and from on the desert terrain, retreating at a time and then suddenly attacking to regain control of small towns and villages in the Eastern rebel held parts of Libya — had led to the technical becoming a vehicle of choice for both sides.

Given the slow speed and the coarse resolution this was not a feasible technique for printing large images, but could usefully print a small logo onto a letterhead and then the following letter, all in a single unattended print run without changing the print element.

* Given a small, privileged set of inputs ( e. g., reserved words for a compiler ), the permutation table can be adjusted so that those inputs yield distinct hash values, producing what is called a perfect hash function.

Given that the businesses in Miami Springs had always relied upon the large disposable incomes of the employees of the large airline carriers, the bankruptcy of both corporations in the same year created a chain reaction, eventually causing many small businesses to close their doors.

Given the borough's small size, as well as the county's small population, the presence of business and government remain limited.

Given the price of 1 / 32 Mark for six small fruit pies ( as seen in Dragonsinger ), it places the value at around $ 20 to the Mark.

: Little Hope Given Brain-Damaged Man ( A brain-damaged man is unlikely to recover, or a brain-damaged man is causing another situation to have little hope of resolution, or someone gave a brain-damaged man to a small girl named Hope.

Given any neighborhood of, we can choose a small positive and a small of either sign to get values both greater and less than.

Given Canada's small market and its position next to the dominant producer of feature films, the Canadian film industry receives substantial assistance from the government.

Given the prevalence of childhood sexual abuse, even if only a small proportion are repressed and only some of them are subsequently recovered, there should be a significant number of corroborated cases.

Given the small likelihood of his older brothers producing heirs, and William's relative youth and good health, it had long been considered extremely likely that he would become King in due course.

" Given that the parched region of the Gran Chaco ( largely uninhabited ) had been under dispute between Bolivia and Paraguay ever since the creation of both republics, each proceeded to establish a line of small garrisons ( fortines ), simply to establish a national presence and press their claims.

Given small differences in policies, the same type of software can produce radically different social outcomes.

Given the small size of the Netherlands, the latter co-operation is not likely to be symmetrical.

She also had a small role as a call girl hired by Al Pacino's character in Oliver Stone's sports drama Any Given Sunday, as well as a key supporting role in Woody Allen's The Curse of the Jade Scorpion.

Given a small angular displacement, the vessel may return to its original position ( stable ), move away from its original position ( unstable ), or remain where it is ( neutral ).