Let $(X, \mathcal A,\mu)$ be a measure space, and $0<p<\infty$
Definition: The weak $L^p-$space on $(X, \mathcal A,\mu)$
denoted $L^{p,\infty}(X, \mu)$ is defined as the set of all $\mu$-measurable functions $f$ such that:
$$\|f\|_{L^{p,\infty}} = \sup\{ t\mu\left(\{x\in X: |f(x)|>t\}\r...
The voting about semicontinuity tag seems mostly in favor of Michael Greinecker's suggestion. Perhaps we can wait a bit and then create the new tag.
Perhaps semicontinuous-functions AND semicontinuous-multifunctions AND semicontinuous-decompositions, although I suspect this last one is a bit too narrow for current topics of interest. Regardless, I think it would be useful to separate out basic real analysis type questions from the multifunction stuff. It also occurs to me that it might be better to use "semicontinuous" (alone or with other words) than "semicontinuity", to assist non-native English speakers, since the usage one almost always sees in definitions and theorems is "semicontinuous", and rarely "semicontinuity". — Dave L. RenfroNov 26 at 14:10
The Radon-Nikodym derivative $\frac{dQ_T}{dQ_B}$ to change the measure from $Q_B$ to $Q_T$ can be obtained by considering the expectations
$\mathbb{E}^{Q_T} [\frac{P(t; T)V(T)}{P(T; T)}|\mathcal{F}_t]= \mathbb{E}^{Q_B} [\frac{P (t; T)V (T)}{P(T; T)}\frac{dQ_T}{dQ_B}
|\mathcal{F}_t]=\mathbb{E}^{Q...
Let $(X, \mathcal A,\mu)$ be a measure space, and $0<p<\infty$
Definition: The weak $L^p-$space on $(X, \mathcal A,\mu)$
denoted $L^{p,\infty}(X, \mu)$ is defined as the set of all $\mu$-measurable functions $f$ such that:
$$\|f\|_{L^{p,\infty}} = \sup\{ t\mu\left(\{x\in X: |f(x)|>t\}\r...
