0
Lusin's theorem says that every measurable function f is a continuous function on nearly all its domain.
It is given that f measurable. This tells us that it is bounded on the complement of some open set of arbitrarily small measure. Now we redefine ƒ to be 0 on this open set. If needed we can assume that ƒ is bounded and therefore integrable.
Now continuous functions are dense in L1([a, b]) so there exists a sequence of continuous functions an tending to ƒ in the L1 norm. If we need to, we can consider a subsequence.
We also assume that an tends to ƒ almost everywhere. Now Egorov's theorem tells us that that an tends to ƒ uniformly except for some open set of arbitrarily small measure. Since uniform limits of continuous functions are continuous, the theorem is proved.
Wiki User
∙ 14y ago
Wiki User
∙ 7y agoLami's theorem states that if three concurrent forces act on a body keeping it in Equilibrium, then each force is proportional to the sine of the angle between the other two forces.
Let P, Q and R be the three forces acting at a point O.
Since OP, OQ and OR are vectors, they can be arranged "nose to tail". Then since the forces are in equilibrium, they form a closed triangle.
Applying the sine rule to the triangle, P/sin[pi - angle(QOR)] = Q/sin[pi- angle(ROP)] = R/sin[pi- angle(POQ)]
Then, since sin(pi - x) = sin(x)
P/sin[angle(QOR)] = Q/sin[angle(ROP)] = R/sin[angle(POQ)]
Add your answer:
Earn +20 pts
State and prove Arzela Ascoli theorem?
I will give a link that explains and proves the theorem.
How do you prove theorem 3.6.1?
Theorem 8.11 in what book?
Prove Hall's theorem from Tutte' theorem graph theory?
in this theorem we will neglect the given resistance and in next step mean as second step we will solve
State and prove stokes theorem?
You can find an introduction to Stokes' Theorem in the corresponding Wikipedia article - as well as a short explanation that makes it seem reasonable. Perhaps you can find a proof under the links at the bottom of the Wikipedia article ("Further reading").
Select the postulate or theorem that could be used to prove QRT STR?
Well, this will depend on the length of the sides of the triangle for what postulate or theorem you will be using.
State and prove Arzela Ascoli theorem?
I will give a link that explains and proves the theorem.
State and prove fundamental theorem of cyclic groups?
..?
Can a corollary be used to prove a theorem?
Yes, the corollary to one theorem can be used to prove another theorem.
How do you prove theorem 3.6.1?
Theorem 8.11 in what book?
How do you find the standard form after you have used the De Moivre's theorem?
(cos0 + i sin0) m = (cosm0 + i sinm0)
How do you solve a remainder theorem?
You cannot solve a theorem: you can prove the theorem or you can solve a question based on the remainder theorem.
What theorem can you use to prove that AEB is congruent to CED?
asa theorem
What elements are necessary for a geometric proof?
A theorem to prove. A series of logical statements. A series of reasons for the statements. answer theorem to prove
What theorem is used to prove a segment is a bisector?
A segment need not be a bisector. No theorem can be used to prove something that may not be true!
which congruence postulate or theorem would you use to prove MEX?
HL congruence theorem
Prove theorem 11.5 for rectangles?
Q.e.d.
State and prove convolution theorem for fourier transform?
Convolution TheoremsThe convolution theorem states that convolution in time domain corresponds to multiplication in frequency domain and vice versa:Proof of (a):Proof of (b):
