# What are the closure properties of LL(k) languages?

Suppose I have two LL languages $$L_1, L_2$$, both describable by LL($$k$$) grammars for the same $$k$$, and regular language $$R$$. Which of the following are also LL languages, and can they be described by LL($$k$$) grammars?

• $$L_1 \cup L_2$$ (union)
• $$L_1 \circ L_2$$ (concatenation)
• $$L_1^*$$ (Kleene star)
• $$L_1 \cap R$$ (intersection with a regular language)