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Page "Shape of the Universe" ¶ 18
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If and you
He said: `` If it's all right with you, Mr. Morgan, I'll sleep out here on the couch.
He added, `` If this doesn't work out, the three of you barricade yourself in the house and talk terms with them ''.
If you want to see '' --
If you were a man '' --
If you ever try anything without my orders I'll kill you ''.
`` If you hadn't I'd have killed you ''.
If you take the one, you'd better take both ''.
If you don't leave this country within 3 days, your life will be taken the same as Powell's was.
If we was both armed, you wouldn't talk so tough ''.
`` If you spot Carmer give a yell before you move in ''.
I showed her the shower and tub, and she said, smiling, `` If you really don't mind, I think I'll get clean in the shower, then soak for a few minutes in your tub.
If I even hint at it do you think it will matter that you are his nephew -- and not even a blood nephew ''??
If you tell him I made a pass at you he might think you misunderstood something I said or did, so instead of just telling him I made a pass, say I tried to date you and that you agreed so you could prove to him what a louse I really am.
Fruit compote: `` If you think I would understand it '' ; ;
If you want to get them aired ''
`` If you want to see something, he's back on the other side by the trunk of the car ''.

If and measure
Some authors require in addition that μ ( C ) < ∞ for every compact set C. If a Borel measure μ is both inner regular and outer regular, it is called a regular Borel measure.
If μ is both inner regular and locally finite, it is called a Radon measure.
* If G is a locally compact Hausdorff topological group and μ its Haar measure, then the Banach space L < sup > 1 </ sup >( G ) of all μ-integrable functions on G becomes a Banach algebra under the convolution xy ( g ) = ∫ x ( h ) y ( h < sup >− 1 </ sup > g ) dμ ( h ) for x, y in L < sup > 1 </ sup >( G ).
If are independent and identically distributed random variables, each with a standard Cauchy distribution, then the sample mean has the same standard Cauchy distribution ( the sample median, which is not affected by extreme values, can be used as a measure of central tendency ).
If the number of counts is not very large, it is more accurate to measure the time interval for a predetermined number of occurrences, rather than the number of occurrences within a specified time.
If available, inhabitants may take potassium iodide at the rate of 130 mg / day per adult ( 65 mg / day per child ) as an additional measure to protect the thyroid gland from the uptake of dangerous radioactive iodine, a component of most fallout and reactor waste.
# If A is a Lebesgue measurable set, then it is " approximately open " and " approximately closed " in the sense of Lebesgue measure ( see the regularity theorem for Lebesgue measure ).
If swelling is observed, the calf circumference should be measured with a tape measure.
If only the second and third conditions of the definition of measure above are met, and takes on at most one of the values, then is called a signed measure.
A measure μ is monotonic: If E < sub > 1 </ sub > and E < sub > 2 </ sub > are measurable sets with E < sub > 1 </ sub > ⊆ E < sub > 2 </ sub > then
A measure μ is countably subadditive: If E < sub > 1 </ sub >, E < sub > 2 </ sub >, E < sub > 3 </ sub >, … is a countable sequence of sets in Σ, not necessarily disjoint, then
A measure μ is continuous from below: If E < sub > 1 </ sub >, E < sub > 2 </ sub >, E < sub > 3 </ sub >, … are measurable sets and E < sub > n </ sub > is a subset of E < sub > n + 1 </ sub > for all n, then the union of the sets E < sub > n </ sub > is measurable, and
A measure μ is continuous from above: If E < sub > 1 </ sub >, E < sub > 2 </ sub >, E < sub > 3 </ sub >, … are measurable sets and E < sub > n + 1 </ sub > is a subset of E < sub > n </ sub > for all n, then the intersection of the sets E < sub > n </ sub > is measurable ; furthermore, if at least one of the E < sub > n </ sub > has finite measure, then
If μ is a positive measure, then N is null ( or zero measure ) if its measure μ ( N ) is zero.
If μ is not a positive measure, then N is μ-null if N is | μ |- null, where | μ | is the total variation of μ ; equivalently, if every measurable subset A of N satisfies μ ( A )
If we acknowledge the fact that we only can measure a probability with some error of measurement attached, we still get into problems as the error of measurement can only be expressed as a probability, the very concept we are trying to define.
If you measure the three qubits, you will observe a three-bit string.
If the overall system is pure, the entropy of one subsystem can be used to measure its degree of entanglement with the other subsystems.
If μ is a complex-valued countably additive Borel measure, μ is regular iff the non-negative countably additive measure | μ | is regular as defined above.

If and circumferences
If AB be the diameter of a semicircle and N any point on AB, and if semicircles be described within the first semicircle and having AN, BN as diameters respectively, the figure included between the circumferences of the three semicircles is Archimedes called " αρβελοσ "; and its area is equal to the circle on PN as diameter, where PN is perpendicular to AB and meets the original semicircle in P.

If and circles
If the dominant country's influence is felt in social and cultural circles, such as " foreign " music being popular with young people, it may be described as cultural imperialism.
If the parameter " dopefish " is added to the executable, a sample of burping is heard and Scott's Mystical Head is seen spinning in circles on the screen.
If we draw both circles, two new points are created at their intersections.
* If four arbitrary points A, B, C, D are given that do not form an orthocentric system, then the nine-point circles of ABC, BCD, CDA and DAB concur at a point.
* If four points A, B, C, D are given that form a cyclic quadrilateral, then the nine-point circles of ABC, BCD, CDA and DAB concur at the anticenter of the cyclic quadrilateral.
( If they are not orientable the natural fibration by circles is not necessarily a Seifert fibration: the problem is that some fibers may " reverse orientation "; in other words their neighborhoods look like fibered solid Klein bottles rather than solid tori .< ref > Ronald Fintushel, Local S < sup > 1 </ sup > actions on 3-manifolds, Pacific J. o. M. 66 No1 ( 1976 ) 111-118, http :// projecteuclid. org /...) The classification of such ( oriented ) manifolds is given in the article on Seifert fiber spaces.
* If a circle q passes through two distinct points A and A ', inverses with respect to a circle k, then the circles k and q are orthogonal.
* If the circles k and q are orthogonal, then a straight line passing through the center O of k and intersecting q, does so at inverse points with respect to k.
If the radical center lies outside of all three circles, then it is the center of the unique circle ( the radical circle ) that intersects the three given circles orthogonally ; the construction of this orthogonal circle corresponds to Monge's problem.
If p / q is between 0 and 1, the Ford circles that are tangent to C can be described variously as
If C and C are tangent Ford circles, then the half-circle joining ( p / q, 0 ) and ( r / s, 0 ) that is perpendicular to the x-axis is a hyperbolic line that also passes through the point where the two circles are tangent to one another.
If M consists of a circle, and N of two circles, M and N together make up the boundary of a pair of pants W ( see the figure at right ).
If you watch the animation above you will see two circles ( one about half way between the edge and center, and the other on the edge itself ) and a straight line bisecting the disk, where the displacement is close to zero.
If a straight line is considered a degenerate circle with zero curvature ( and thus infinite radius ), Descartes ' theorem also applies to a line and two circles that are all three mutually tangent, giving the radius of a third circle tangent to the other two circles and the line.
If four circles are tangent to each other at six distinct points, and the circles have curvatures k < sub > i </ sub > ( for i = 1, ..., 4 ), Descartes ' theorem says:
If one of the three circles is replaced by a straight line, then one k < sub > i </ sub >, say k < sub > 3 </ sub >, is zero and drops out of equation ( 1 ).
If two circles are replaced by lines, the tangency between the two replaced circles becomes a parallelism between their two replacement lines.
If random sections of the cloth are bound, the result will be a pattern of random circles.
If the cloth is first folded then bound, the resulting circles will be in a pattern depending on the fold used.

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