### The Distance From a Point to a Compact Convex Set

Let $K$ be a compact convex subset of the plane and $\lambda \in \mathbb{C}\backslash K$, then $$dist(\lambda ,K)=\|(\lambda -N_{\mu})^{-1}\|^{-1},$$ where $\mu$ is the Lebesgue measure concentrated on $K$ and $N_{\mu}$ be the multiplication operator on $L^{2}(\mu)$.
{"ft_lang_label":"__label__en","ft_lang_prob":0.63051456,"math_prob":0.9999989,"size":385,"snap":"2021-43-2021-49","text_gpt3_token_len":115,"char_repetition_ratio":0.12073491,"word_repetition_ratio":0.0,"special_character_ratio":0.3194805,"punctuation_ratio":0.09859155,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99999964,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-04T17:46:18Z\",\"WARC-Record-ID\":\"<urn:uuid:1ccbcbb9-bdd6-45df-b18b-16ac29e21946>\",\"Content-Length\":\"22184\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ba6769c7-ebfb-46fc-84e7-f3499c799494>\",\"WARC-Concurrent-To\":\"<urn:uuid:445d7470-b9b2-4cdc-8fba-2a26db9c5fb4>\",\"WARC-IP-Address\":\"167.86.118.250\",\"WARC-Target-URI\":\"https://ejpam.com/index.php/ejpam/article/view/1882\",\"WARC-Payload-Digest\":\"sha1:UEGW5ZWFNJ3YXMOF6S47H4NKYCJQVCT2\",\"WARC-Block-Digest\":\"sha1:QHQL56RRHBPPJFT7VVTXUVXUZPJ2UD76\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964362999.66_warc_CC-MAIN-20211204154554-20211204184554-00146.warc.gz\"}"}