- What is the difference between differentiable and continuous
I have always treated them as the same thing But recently, some people have told me that the two terms are different So now I am wondering, What is the difference between "differentiable" and "
- What is a continuous stochastic process? - Mathematics Stack Exchange
So, there will be a discontinuity at time k Isn't this violating the definition of continuous stochastic process or is it that I have to keep ω ω constant throught out the process ? Also, is ω ω in the definition of continuous stochastic process the outcome at any point of time or is it the string of the outcomes that occurs till time
- is bounded linear operator necessarily continuous?
This property is unrelated to the completeness of the domain or range, but instead only to the linear nature of the operator Yes, a linear operator (between normed spaces) is bounded if and only if it is continuous
- functional analysis - continuity in the strong topology implies . . .
I have to prove that if T: (E, ‖ ⋅ ‖E) → (F, ‖ ⋅ ‖F) is a continuous and linear operator, and xh ⇀ x in E, than Txh ⇀ Tx in F So we know that T is continuous with respect to the strong topologies, and we want to prove that it is also continuous with respect to the weak ones Is there a simple proof of this fact?
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