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First, we introduce some classes of weights.
First, we introduce classes of weights.
Note that the A-class is an extension of some existing classes of weights, such as A r λ -weights, A r -weights, and A r -weights.
For more precise description, let us introduce the following two classes of weights; We note that h given in the above example satisfies h ∈ A ∩ B but h ∉ L 1 ( 0, 1 ).
We introduce the following class of functions which is an extension of the several existing classes of weights, such as A r λ ( E ) -weights, A r (λ, E -weights, and A r (E -weights.
The different classes of weights that can be used for FSTs are the so-called semirings.
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As a final remark, we mention the fact that combining our technique with Ważewski's method [31], following the approach developed by Conley in [18], one can deal with some more general classes of weight functions.
Next we recall some properties of a class of weights we are interested in, and we adapt to weighted framework some known embedding results.
Analogously is defined the class of weights D C ( x ).
However, we need to focus on a smaller class of weights.
Levin and Lubinsky [5, 6] introduced the class of weights on ℝ+ as follows.
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