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i) [mathematical expression not reproducible] attains the infimum in (39) with [zeta] = [?
For well-behaving functions, both the supremum of the values [integral] s(x) dx for all s(x) [less than or equal to] f (x) and the infimum of the values [integral] s(x) dx for all s(x) [greater than or equal to] f (x) coincide--and are equal to the integral.
Although there is not a unique interval extension for a specific real-valued function, any interval extension is valid as long as that when a degenerate interval (an interval with the same infimum and supremum) is plugged into the interval extension the correct value for the real-valued function is retrieved, i.
where the infimum is taken over all irreducible curves passing through at least one of the points [P.
if there exists a sufficiently small [theta], price dispersion (as measured either by the price range between the supremum and the infimum or by differences in percentile price as discussed above) increases with [theta] until R = z.
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and the infimum is taken over all countable collection ([I.
Among their topics are isotropic log-concave measures, bodies with maximal isotropic constant, tail estimates for linear functions, the central limit problem and the thin shell conjecture, and infimum convolution inequalities and concentration.