Some topics concerning analysis on metric spaces and semigroups of operators
نویسنده
چکیده
where the supremum is taken over all open balls B in R which contain x. The supremum may be +∞, so that f ∗ is actually a (nonnegative) extended real-valued function. This is sometimes referred to as the uncentered maximal function, and there are variants defined in terms of balls centered at x, or using cubes instead of balls. A nice feature of f (x) is that it is upper semicontinuous, which is to say that
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