bounded interval การใช้

• The Riemann integral can only integrate functions on a bounded interval.
• Bounded intervals are also commonly known as "'finite intervals " '.
• The bounded intervals converge to a unique real number, denoted by b ^ \ pi.
• In fact, if is a bounded interval, then for all and all the following inequality holds
• The " nested intervals theorem " states that if each is a closed and bounded interval, say
• Applying Theorem 2 ( whose assumptions are verified when p _ { i } is restricted to a bounded interval ) yields
• He also proved the Bolzano Weierstrass theorem and used it to study the properties of continuous functions on closed and bounded intervals.
• This shows that the intersection of ( even an uncountable number of ) nested, closed, and bounded intervals is nonempty.
• Each equality or inequality takes either a point, a bounded interval, or a semi-bounded interval away from it.
• Each equality or inequality takes either a point, a bounded interval, or a semi-bounded interval away from it.
• It includes all Laplace distributions, and as limiting cases it includes all continuous uniform distributions on bounded intervals of the real line.
• Assuming that the Cauchy data U ( defined in the bounded interval [ a, b ] ) and that the domain of f.
• Bounded intervals are bounded sets, in the sense that their diameter ( which is equal to the absolute difference between the endpoints ) is finite.
• The distribution provides an alternative to the beta distribution such that it allows more density to be placed at the extremes of the bounded interval of support.
• Furthermore, every bounded function on a closed bounded interval has a Lebesgue integral and there are many functions with a Lebesgue integral that have no Riemann integral.
• For a bounded interval, the collection of all the moments ( of all orders, from to ) uniquely determines the distribution ( Hausdorff moment problem ).
• Lebesgue integration has the property that every function defined over a bounded interval with a Riemann integral also has a Lebesgue integral, and for those functions the two integrals agree.
• In conjunction with the extreme value theorem, it can be used to find the absolute maximum and minimum of a real-valued function defined on a closed, bounded interval.
• The classification depended on whether the distributions were supported on a bounded interval, on a half-line, or on the whole real line; and whether they were potentially skewed or necessarily symmetric.
• Weierstrass formalized the definition of the continuity of a function, proved the intermediate value theorem and the Bolzano Weierstrass theorem, and used the latter to study the properties of continuous functions on closed bounded intervals.