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In that period, on average, 8,746 classes were closed each year.
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To show the classes are closed under countable composition, we use the following lemma.
Later Libera [3] introduced an integral operator and showed that these two classes are closed under this operator.
We characterize the ordinals which occur as the index of an operator and establish exactly when the defined classes are closed.
The primality of p ensures that the product of two integers neither of which is divisible by p is not divisible by p either, hence the indicated set of classes is closed under multiplication.
Classes are closed now, but I fear not being able to go back when they will reopen".
Classes are closing all the time so I must be doing something right.
The class is closed under convex combinations.
The class is closed under the following operations.
If '>' is a probability conditional for a class of probability functions, and if the class is closed under conditioning, then (5) holds for any probability function in the class, and for any a and c.
Another interesting observation to note from interaction CCS x SCD (in Table 2) is that if a longer school closure duration is selected, then it is preferable to close a school sooner after a class is closed.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com