Implications

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We have the following indirect implication of form equivalence classes:

25 \(\Rightarrow\) 19 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
25 \(\Rightarrow\) 34	clear
34 \(\Rightarrow\) 19	Sur les fonctions representables analytiquement, Lebesgue, H. 1905, J. Math. Pures Appl.

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number	Statement
25:	\(\aleph _{\beta +1}\) is regular for all ordinals \(\beta\).
34:	\(\aleph_{1}\) is regular.
19:	A real function is analytically representable if and only if it is in Baire's classification. G.Moore [1982], equation (2.3.1).

Comment: