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No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.
No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.
No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.
No, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.
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CoachNo, a measurable function may have a finite number of discontinuities (for the Riemann measure), or a countably infinite number of discontinuities (for the Lebesgue measure). It should also be bounded (have some upper and lower bound, or limit, in the domain that is being measured), to be measureable. At least, some unbounded functions are not measurable.
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Are continuous functions integrable?
yes, every continuous function is integrable.
Is a corner continuous?
Yes, a corner is continuous, as long as you don't have to lift your pencil up then it is a continuous function. Continuous functions just have no breaks, gaps, or holes.
Any measurable function can be approximated by simple function?
Yes. For every measurable function, f there's a sequence of simple functions Fn that converge to f m-a.e (wich means for each e>0, there's X' such that Fn|x' -->f|x' and m(X\X')<e).
What is the important similarity between the uniform and normal probability distribution?
They are both continuous, symmetric distribution functions.
What are some similarities and differences between quartic and cubic functions?
The similarities are that they are polynomial functions and therefore continuous and differentiable.A real cubic will has an odd number of roots (and so must have a solution), a quartic has an even number of roots and so may have no solutions.
Are continuous functions integrable?
yes, every continuous function is integrable.
What has the author Krzysztof Ciesielski written?
Krzysztof Ciesielski has written: 'I-density continuous functions' -- subject(s): Baire classes, Continuous Functions, Functions, Continuous, Semigroups
When finding the derivative of a point on a piecewise function does every function in the piecewise function need to be continuous and approach the same limit?
All differentiable functions need be continuous at least.
Are all continuous functions linear?
Not at all.Y = x2 is a continuous function.
Are all functions continuous?
No. Not all functions are continuous. For example, the function f(x) = 1/x is undefined at x = 0.
Are all polynomial funcions continuous?
Yes, all polynomial functions are continuous.
Can all functions be discrete or continuous?
No. There are many common functions which are not discrete but the are not continuous everywhere. For example, 1/x is not continuous at x = 0 (it is not even defined there. Then there are curves with step jumps.
What has the author Jean Schmets written?
Jean Schmets has written: 'Spaces of vector-valued continuous functions' -- subject(s): Continuous Functions, Locally convex spaces, Vector valued functions
What has the author Frederick Bagemihl written?
Frederick Bagemihl has written: 'Meier points and horocyclic Meier points of continuous functions' -- subject(s): Continuous Functions
Is a corner continuous?
Yes, a corner is continuous, as long as you don't have to lift your pencil up then it is a continuous function. Continuous functions just have no breaks, gaps, or holes.
Is the infinite sum of continuous function continuous?
An infinite sum of continuous functions does not have to be continuous. For example, you should be able to construct a Fourier series that converges to a discontinuous function.
Any measurable function can be approximated by simple function?
Yes. For every measurable function, f there's a sequence of simple functions Fn that converge to f m-a.e (wich means for each e>0, there's X' such that Fn|x' -->f|x' and m(X\X')<e).
