lower semicontinuous मीनिंग इन हिंदी

उदाहरण वाक्य

1. The indicator function of any open set is lower semicontinuous.
2. One can differentiate many continuity concepts, primarily closed graph property and upper and lower semicontinuous real-valued function ).
3. Nevertheless, lower semicontinuous multifunctions usually possess continuous selections as stated in the Michael selection theorem, which provides another characterisation of paracompact spaces.
4. Every positive form ? extends uniquely to the linear span of non-negative bounded lower semicontinuous functions " g " by the formula
5. Let X be a normal topological space and let g, h \ colon X \ to \ mathbb { R } be functions with g upper semicontinuous, h lower semicontinuous and g \ leq h.
6. "A sequentially weakly lower semicontinuous coercive functional on a reflexive Banach space has a minimizer . " A slight generalization appears in Giusti ( 2003 ), " Direct methods in the calculus of variations ", World Scientific.
7. However, in convex analysis, the term " indicator function " often refers to the characteristic function, and the characteristic function of any " closed " set is lower semicontinuous, and the characteristic function of any " open " set is upper semicontinuous.
8. Using lower and upper Hausdorff uniformity we can also define the so-called "'upper "'and "'lower semicontinuous maps in the sense of Hausdorff "'( also known as "'metrically lower / upper semicontinuous maps "').
9. If X = \ mathbb R ^ n is a Euclidean space ( or more generally, a metric space ) and \ Gamma = C ( [ 0, 1 ], X ) is the space of curves in X ( with the length L ( \ alpha ), is lower semicontinuous.