Is pumping lemma for regular languages “closed” against Kleene star?

If I have an infinite language $L$ which fulfills the Pumping lemma for regular languages, does $L^*$ also fulfill the same conditions?

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 What have you tried? – Raphael♦ Feb 16 at 15:14 1. if the first word of the Concatenation> n so that we can do a pumping – user6885 Feb 16 at 15:30 2.word of the Concatenation

In order to show the pumping property of a string like $x_1x_2 \dots x_n$, where each $x_i\in L$ you can distinguish two cases. Either $x_1$ is "short", which means you can pump $x_1$ completely and stay within $L^*$, or $x_1$ is "long" and you can pump "inside" $x_1$.