Then, applying the triangle inequality to both sides, using ( 5 ) and the fact that as well as are non-negative we obtain

Then f + g is in L < sup > p </ sup >( S ), and we have the triangle inequality

Then Jensen's inequality can be applied to get

Then f is called weak if there exists a constant C such that the distribution of f satisfies the following inequality for all t > 0:

Then the following interpolation inequality holds for all r between p and q and all f ∈ L < sup > r </ sup >:

Then the inequality above needs to be replaced with

Suppose that r < R. Then, we have the following inequality:

Then the Ky Fan inequality can be written as

Then the inequality

Then by the triangle inequality the polygon perimeter > AB + AX + XB = AB + AC + CX + XB ≥ AB + AC + BC.

Then will come nine other states in the order of their admission to the union.

Then g ( E ) is called the density of states if the energy spectrum is continuous.

Then define a process Y, such that each state of Y represents a time-interval of states of X.

Then Noether's theorem states that the following quantity is conserved,

Then Michael Palin came out as an over the top announcer who eventually states that he only ever wanted to be a lumberjack.

Then the Black formula states the price for a European call option of maturity T on a futures contract with strike price K and delivery date T ( with ) is

Then in 1991, the Soviet Union collapsed, replaced by the Russian Federation and several ex-Soviet Republics became independent states.

Then, the Riemann-Roch theorem states that

Then the 10th Amendment, the one where they say leave the rest for the states to decide, he was a guy with no self-esteem.

Then the Riemann – Roch theorem states: if g is a genus of X,

Then Prime-Minister, Pierre Mendès-France attempted to placate the treaty's detractors by attempting to ratify additional protocols with the other signatory states.

Then the theorem states that for analytic functions f, if

When Claire insists that she is not an alcoholic, Agnes states sarcastically, “ that ’ s very nice .” Then she lists times that Claire has vomited, fallen down, and called from the club to have someone come and get her.

Then the ratio test states that:

Then, the bound states themselves form a condensate.

Elliott considers her greatest honor to be having Kenneth Clark write the foreword to the book " A Class Divided Then and Now " by William Peters in which he states, "... Jane Elliott's contribution demonstrates that it is possible to educate and produce a class of human beings united by understanding, acceptance, and empathy.

Then he or she states the Omer-count in terms of both total days and weeks and days.

Then he suggested dividing Germany into 3 states, all of which would be included in a new European customs union.

Suppose that M is a complex matrix of order n, whose entries are bounded by | M < sub > ij </ sub >| ≤ 1, for each i, j between 1 and n. Then Hadamard's determinant bound states that

Then he meets the troll king, who states that he has been a troll, not a man, most of his life.

Then Gerd shows up, and states that evil forces will prevail if he leaves.

While preparing for one last fight against the army of the Senior Partners, Illyria states that he has only minutes to live with Gunn quoting, " Then let's make them memorable.

Then, extreme samurais from 3 states ( Mito, Chōshū and Tosa ) were competing with each other carrying out terrorist actions against those who they believed were against anti-foreigner ideals.

Then with the 1971 Oregon v. Mitchell decision, the Supreme Court ruled that state and local elections did not have to abide by the lowered voting age, though there would have to be dual elections in the 47 states where the lower federal voting age was not valid.

Then Little Billy began shouting orders to round up the ponies and fill the water buckets and for the cooks to hurry up with the meal.

Then, helpfully, as she merely stared at him in weary silence, `` Maybe you could write it down for me, huh??

Then they were tumbling again, and the big man reached into the same pocket he had gone for earlier, and came up with a vicious switchblade.

`` Then I return to the United States for engagements at the Hollywood Bowl and in Philadelphia '', he added.

Then Miriam varied the senseless psychological warfare by suddenly withdrawing a suit for separate maintenance that had been pending, and asking for divorce on the grounds of cruelty, with the understanding that Wright would not contest it.

My own stern hand has rent the ancient bond, And thereof shall the ending not have end: But not for me, that loved her, to be fond Lightly to please me with a newer friend Then hold it more than bravest-feathered song, That I affirm to thee, with heart of pride, I knew not what did to a friend belong Till I stood up, true friend, by thy true side ; ;

Then Meltzer's voice, quiet, calm, strong, started the Kaddish, the prayer for the dead.

Then they returned to their hotel and got ready for bed.

Then he kept Blackman awake for more than an hour while he did an imaginary dialogue between his wife and himself in which, discussing the evening, he was continually berated.

Then we have surviving at least one instance of a poem prepared for another, in Naturam non Pati Senium, and perhaps also the De Idea Platonica.

Then followed a period in which he wrote reviews for The New York Times Book Review, The Commonweal, Commentary, had a small piece in Partisan Review, and moved on to Hudson, The Village Voice, and Exodus.

Then a full-time planning office will be established in Rome to work with a five-member Georgia Tech research staff for development of an area planning and industrial development program.

Then Goodbody will hand over a minimum of $15.5 million for developing the spacious Graves Tract to house the center.

Then, to conclude on an indeterminate note: `` Nevertheless, if fallout increased substantially, or remained high for a long time, it would become far more important as a potential health hazard in this country and throughout the world ''.

Then, abandoning the studies in the face of their promising outlook for all concerned, B. & O. entered on-again-off-again negotiations with C. & O. which resulted in the present situation.

Then they were given 1/2 to 1-1/2 avocados per day as a substitute for part of their dietary fat consumption.

Then, after emasculation, he was eased up for a couple of weeks.

Then you'll want terry cloth towels for mopping up.

Then, for the above parasites, feed continuously at these levels: Feeder cattle -- 2-5 grams of phenothiazine daily ; ;

Then, too, European drivers have reputations for being somewhat crazy on the road and some Americans are not particularly keen on getting mixed up with them.

Then, for the first time since his arrest, a glint of spirit lit Barco's eyes.

Then, I remembered that the girls had had a banana for dessert every day for the last week.

Then, having wrapped the lot in an afghan my dog customarily slept on, you lammed out the front door, considerately leaving it open for neighbors to discover.